DIGITAL SIGNAL PROCESSING - iare.ac.in · PDF file1 DEPT OF ECE DIGITAL SIGNAL PROCESSING LAB MANUAL Subject Code: A60493 Regulations : R15 – JNTUH Class : III Year II Semester (ECE)

1 DEPT OF ECE

DIGITAL SIGNAL PROCESSING

LAB MANUAL

Subject Code : A60493

Regulations : R15 – JNTUH

Class : III Year II Semester (ECE)

Mrs .C. Devi supraja

Assistant Professor

Department of Electronics & Communication Engineering

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)

Dundigal – 500 043, Hyderabad

Prepared by Dr. Prashant Pradhan

Professor

Mrs. G. Mary

Swarnalatha

Assistant Professor

Mr.V Naresh Kumar

Assistant Professor

2 DEPT OF ECE


Dundigal - 500 043, Hyderabad

Electronics & Communication Engineering

Vision

To produce professionally competent Electronics and Communication Engineers capable of

effectively and efficiently addressing the technical challenges with social responsibility.

Mission The mission of the Department is to provide an academic environment that will ensure high

quality education, training and research by keeping the students abreast of latest developments in

the field of Electronics and Communication Engineering aimed at promoting employability,

leadership qualities with humanity, ethics, research aptitude and team spirit.

Quality Policy Our policy is to nurture and build diligent and dedicated community of engineers providing a

professional and unprejudiced environment, thus justifying the purpose of teaching and

satisfying the stake holders.

A team of well qualified and experienced professionals ensure quality education with its

practical application in all areas of the Institute.

Philosophy The essence of learning lies in pursuing the truth that liberates one from the darkness of

ignorance and Institute of Aeronautical Engineering firmly believes that education is for

liberation.

Contained therein is the notion that engineering education includes all fields of science that plays

a pivotal role in the development of world-wide community contributing to the progress of

civilization. This institute, adhering to the above understanding, is committed to the development

of science and technology in congruence with the natural environs. It lays great emphasis on

intensive research and education that blends professional skills and high moral standards with a

sense of individuality and humanity. We thus promote ties with local communities and

encourage transnational interactions in order to be socially accountable. This accelerates the

process of transfiguring the students into complete human beings making the learning process

relevant to life, instilling in them a sense of courtesy and responsibility.

3 DEPT OF ECE


Dundigal, Hyderabad - 500 043


Program Outcomes

PO1 Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering

specialization to the solution of complex engineering problems.

PO2

Identify, formulate, review research literature, and analyze complex engineering problems reaching

substantiated conclusions using first principles of mathematics, natural sciences, and engineering

sciences.

PO3

Design solutions for complex engineering problems and design system components or processes that

meet the specified needs with appropriate consideration for the public health and safety, and the

cultural, societal, and environmental considerations.

PO4 Use research-based knowledge and research methods including design of experiments, analysis and

interpretation of data, and synthesis of the information to provide valid conclusions.

PO5

Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools

including prediction and modelling to complex engineering activities with an understanding of the

limitations.

PO6 Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and

cultural issues and the consequent responsibilities relevant to the professional engineering practice.

PO7 Understand the impact of the professional engineering solutions in societal and environmental contexts,

and demonstrate the knowledge of, and need for sustainable development.

PO8 Apply ethical principles and commit to professional ethics and responsibilities and norms of the

engineering practice.

PO9 Function effectively as an individual, and as a member or leader in diverse teams, and in

multidisciplinary settings.

PO10

Communicate effectively on complex engineering activities with the engineering community and with

society at large, such as, being able to comprehend and write effective reports and design

documentation, make effective presentations, and give and receive clear instructions.

PO11

Demonstrate knowledge and understanding of the engineering and management principles and apply

these to one‟s own work, as a member and leader in a team, to manage projects and in multidisciplinary

environments.

PO12 Recognize the need for, and have the preparation and ability to engage in independent and life-long

learning in the broadest context of technological change.

Program Specific Outcomes

PSO1

Professional Skills:An ability to understand the basic concepts in Electronics & Communication

Engineering and to apply them to various areas, like Electronics, Communications, Signal processing,

VLSI, Embedded systems etc., in the design and implementation of complex systems.

PSO2

Problem-solving skills:An ability to solve complex Electronics and communication Engineering

problems, using latest hardware and software tools, along with analytical skills to arrive cost effective

and appropriate solutions.

PSO3

Successful career and Entrepreneurship:An understanding of social-awareness & environmental-

wisdom along with ethical responsibility to have a successful career and to sustain passion and zeal for

real-world applications using optimal resources as an Entrepreneur.

4 DEPT OF ECE




ATTAINMENT OF PROGRAM OUTCOMES

& PROGRAM SPECIFIC OUTCOMES

S. No. Experiment Program

Outcomes

Attained

Program Specific

Outcomes Attained

Using MATLAB

1 Generation of Sinusoidal waveform/signal

based on recursive difference equation PO1, PO2, PO5 PSO1, PSO2

2 To find DFT/IDFT of given DT signal PO1, PO2, PO5 PSO1, PSO2

3 To find frequency response of a given system given

in (Transfer Function) PO1, PO2, PO5 PSO1, PSO2

4 Implementation of FFT of given sequence

(DIT/DIF) PO1, PO2, PO5 PSO1, PSO2

5 Determination of Power Spectrum of a given signal PO1, PO2, PO5 PSO1, PSO2

6 Implementation of LP FIR filters for a given

sequence PO1, PO2, PO5 PSO1, PSO2

7 Implementation of HP FIR filters for a given sequence

PO1, PO2, PO5 PSO1, PSO2

8 Implementation of LP IIR filters for a given sequence


9 Implementation of HP IIR filters for a given sequence


10 Generation of Sinusoidal signal through filtering PO1, PO2, PO5 PSO1, PSO2

11 Implementation of Decimation Process PO1, PO2, PO5 PSO1, PSO2

12 Implementation of Interpolation Process PO1, PO2, PO5 PSO1, PSO2

13 Implementation of I/D sampling rate converters PO1, PO2, PO5 PSO1, PSO2

14 Impulse response of first order and second order systems


Using DSP KIT 15

N-Point DFT PO1, PO2, PO5,

PO11 PSO1, PSO2

16 Generation of Sine Wave using C6713 DSK

PO1, PO2, PO5, PO11

PSO1, PSO2

5 DEPT OF ECE

ATTAINMENT OF PROGRAM OUTCOMES

& PROGRAM SPECIFIC OUTCOMES

S. No. Experiment

Program

Outcomes

Attained

Program Specific Outcomes Attained

17 FIR filter using Rectangular window (low pass) PO1, PO2, PO5,

PO11 PSO1, PSO2

18 FIR filter using Kaiser Window (high pass) PO1, PO2, PO5,

PO11 PSO1, PSO2

19 IIR filter using Butterworth Approximation (low pass)

PO1, PO2, PO5,

PO11 PSO1, PSO2

Content Beyond Syllabi

1 Linear Convolution using CC Studio PO1, PO2 PSO1

2 Circular Convolution using CC Studio PO1, PO2 PSO1

6 DEPT OF ECE



CCeerrttiiffiiccaattee

This is to Certify that it is a bonafied record of Practical work done by

Sri/Kum. _____________________________________ bearing

the Roll No. ______________________ of ____________ Class

_______________________________________ Branch in the

____________________________ laboratory during the Academic

year ___________________ under our supervision.

Head of the Department Lecture In-Charge

External Examiner

Internal Examiner

7 DEPT OF ECE




DIGITAL SIGNAL PROCESSING LABORATORY

Course Overview:

This laboratory course builds on the lecture course "Digital Signal Processing" which is mandatory for all

students of electronics and communication engineering. This course is devoted to the application of

digital signal processing techniques to implement various types of signal filtering, including FIR and IIR

filters.And use the Fast Fourier Transform in a variety of applications. Students gain experience in how

such digital processes are implemented in practice using MATLAB and also study a standard DSP

platform.

Course Out Comes:

1. Analyze signals using the discrete Fourier transform (DFT).

2. Understand the implementation of FFT algorithm for efficient computation of the DFT.

3. Design digital IIR filters by designing prototypical analog filters and then applying analog to

digital conversion techniques such as the bilinear transformation.

4. Design digital FIR filters using the window method. 5. Alter the sampling rate of a signal using decimation and interpolation.

8 DEPT OF ECE




INSTRUCTIONS TO THE STUDENTS

1. Students are required to attend all labs.

2. Students should work individually in the hardware and software laboratories.

3. Students have to bring the lab manual cum observation book, record etc along

with them whenever they come for lab work.

4. Should take only the lab manual, calculator (if needed) and a pen or pencil to the

work area.

5. Should learn the prelab questions. Read through the lab experiment to familiarize

themselves with the components and assembly sequence.

6. Should utilize 3 hour‟s time properly to perform the experiment and to record the

readings. Do the calculations, draw the graphs and take signature from the

instructor.

7. If the experiment is not completed in the stipulated time, the pending work has to

be carried out in the leisure hours or extended hours.

8. Should submit the completed record book according to the deadlines set up by the

instructor.

9. For practical subjects there shall be a continuous evaluation during the semester

for 25 sessional marks and 50 end examination marks.

10. Out of 25 internal marks, 15 marks shall be awarded for day-to-day work and 10

marks to be awarded by conducting an internal laboratory test.

9 DEPT OF ECE




DIGITAL SIGNAL PROCESSING LABORATORY

Recommended Systems/Software Requirements:

Intel based desktop PC with minimum of 166 MHZ or faster processor with at least 64 MB RAM

and 100MB free disk space. MATLAB.

S.

No. List of Experiments Page No. Date Remarks

Introduction to MATLAB

1 Generation of Sinusoidal waveform/signal based on recursive

difference equation

2 To find DFT/IDFT of given DT signal

3 To find frequency response of a given system given in (Transfer

Function)

4 Implementation of FFT of given sequence (DIT/DIF)

5 Determination of Power Spectrum of a given signal

6 Implementation of LP FIR filters for a given sequence

7 Implementation of HP FIR filters for a given sequence

8 Implementation of LP IIR filters for a given sequence

9 Implementation of HP IIR filters for a given sequence

10 Generation of Sinusoidal signal through filtering

11 Implementation of Decimation Process

12 Implementation of Interpolation Process

13 Implementation of I/D sampling rate converters

14 Impulse response of first order and second order systems

USING DSP KIT Introduction to DSPCHIP-TMS320C6713

1 N-Point DFT

2 Generation of Sine Wave using C6713 DSK

3 FIR filter using Rectangular window (low pass)

4 FIR filter using Kaiser Window (high pass)

5 IIR filter using Butterworth Approximation (low pass)

CONTENT BEYOND THE SYLLABUS

1 Linear Convolution using CC Studio

2 Circular Convolution using CC Studio

*Content beyond the university prescribed syllabi

10 DEPT OF ECE

INTRODUCTION TO MATLAB

MATLAB (MATRIX LABORATORY):

MATLAB is a software package for high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation. Typical uses include the following

Math and computation

Algorithm development

Data acquisition

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

Application development, including graphical user interface building

At its core ,MATLAB is essentially a set (a “toolbox”) of routines (called “m files” or “mix

files”)that sit on your computer and a window that allows you to create new variables with

names (e.g. voltage and time) and process those variables with any of those routines (e.g. plot

voltage against time, find the largest voltage, etc). It also allows you to put a list of your

processing requests together in a file and save that combined list with a name so that you can run

11 DEPT OF ECE

all of those commands in the same order at some later time. Furthermore, it allows you to run

such lists of commands such that you pass in data and/or get data back out (i.e. the list of

commands is like a function in most programming languages). Once you save a function, it

becomes part of your toolbox (i.e. it now looks to you as if it were part of the basic toolbox that

you started with). For those with computer programming backgrounds: Note that MATLAB runs

as an interpretive language (like the old BASIC). That is, it does not need to be compiled. It

simply reads through each line of the function, executes it, and then goes on to the next line. (In

practice, a form of compilation occurs when you first run a function, so that it can run faster the

next time you run it.)

The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide

easy access to matrix software developed by the LINPACK and EISPACK projects. Today,

MATLAB engines incorporate the LAPACK and BLAS libraries, embedding the state of the art

in software for matrix computation. MATLAB has evolved over a period of years with input

from many users. In university environments, it is the standard instructional tool for introductory

and advanced courses in mathematics, engineering, and science. In industry, MATLAB is the

tool of choice for high-productivity research, development, and analysis.

MATLAB features a family of add-on application-specific solutions called toolboxes. Very

important to most users of MATLAB, toolboxes allow learning and applying specialized

technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems. Areas in which

toolboxes are available include Image processing, signal processing, control systems, neural

networks, fuzzy logic, wavelets, simulation, and many others.

The main features of MATLAB

Advance algorithm for high performance numerical computation, especially in the Field

matrix algebra

A large collection of predefined mathematical functions and the ability to define one‟s own

functions.

Two-and three dimensional graphics for plotting and displaying data

A complete online help system

Powerful, matrix or vector oriented high level programming language for individual

applications.

12 DEPT OF ECE

Toolboxes available for solving advanced problems in several application areas

MATLAB Windows:

MATLAB works with through three basic windows

COMMAND WINDOW:

This is the main window .it is characterized by MATLAB command prompt >> when you

launch the application program MATLAB puts you in this window all commands including

those for user-written programs ,are typed in this window at the MATLAB prompt

GRAPHICS WINDOW:

the output of all graphics commands typed in the command window are flushed to the graphics

or figure window, a separate gray window with white background color the user can create as

many windows as the system memory will allow

EDIT WINDOW:

This is where you write edit, create and save your own programs in files called M files.

INPUT-OUTPUT:

MATLAB supports interactive computation taking the input from the screen and flushing, the

output to the screen. In addition it can read input files and write output files

DATA TYPE:

The fundamental data –type in MATLAB is the array. It encompasses several distinct data

objects- integers, real numbers, matrices, character strings, structures and cells. There is no need

to declare variables as real or complex, MATLAB automatically sets the variable to be real.

DIMENSIONING:

Dimensioning is automatic in MATLAB. No dimension statements are required for vectors or

arrays .we can find the dimensions of an existing matrix or a vector with the size and length

commands.

The functional unit of data in any MATLAB program is the array. An array is acollection of data

values organized into rows and columns, and known by a single name.MATLAB variable is a

region of memory containing an array, which is known by a userspecifiedname. MATLAB

13 DEPT OF ECE

variable names must begin with a letter, followed by anycombination of letters, numbers, and the

underscore( _ ) character. Only the first 31characters are significant; if more than 31 are used,

the remaining characters will beignored. If two variables are declared with names that only differ

in the 32nd character,MATLAB will treat them as same variable.

Spaces cannot be used in MATLAB variable names, underscore letters can be substitutedto

create meaningful names.It is important to include a data dictionary in the header of any program

that you write. Adata dictionary lists the definition of each variable used in a program. The

definitionshould include both a description of the contents of the item and the units in which it

ismeasured.

MATLAB language is case-sensitive. It is customary to use lower-case letters forordinary

variable names.The most common types of MATLAB variables are double and char.MATLAB

is weakly typed language. Variables are not declared in a program before it isused.

MATLAB variables are created automatically when they are initialized. There are threecommon

ways to initialize variables in MATLAB:

- Assign data to the variable in an assignment system.

- Input data into the variable from the keyboard.

- Read data from a file.

The semicolon at the end of each assignment statement suppresses the automatic echoingof

values that normally occurs whenever an expression is evaluated in an assignmentstatement.

HOW TO INVOKE MATLAB?

Double Click on the MATLAB icon on the desktop.

You will find a Command window where in which you can type the commands and see

theoutput. For example if you type PWD in the command window, it will print current

workingdirectory.

If you want to create a directory type mkdirmydirin the command window, It will create

adirectory called pes.

If you want delete a directory type rmdirmydirin the command window.

HOW TO OPEN A FILE IN MATLAB?

14 DEPT OF ECE

Go to File ->New->M-File and click

Then type the program in the file and save the file with an extension of .m. While giving

filename we should make sure that given file name should not be a command. It is better to the

file name as myconvlution.

HOW TO RUN A MATLAB FILE?

Go to Debug->run and click

Where to work in MATLAB?

All programs and commands can be entered either in the a)Command window b) As an M file

using Mat lab editor Note: Save all M files in the folder 'work' in the current directory.

Otherwise you have to locate the file during compiling. Typing quit in the command prompt>>

quit, will close MATLAB Mat lab Development Environment. For any clarification regarding

plot etc, which are built in functions type help topic i.e. help plot

BASIC INSTRUCTIONS IN MAT LAB

T = 0: 1:10 This instruction indicates a vector T which as initial value 0 and final value 10

with an increment of 1 Therefore T = [0 1 2 3 4 5 6 7 8 9 10]

F= 20: 1: 100 Therefore F = [20 21 22 23 24 ……… 100]

T= 0:1/pi: 1 Therefore T= [0, 0.3183, 0.6366, 0.9549]

zeros (1, 3) The above instruction creates a vector of one row and three columns whose

values are zero Output= [0 0 0]

zeros( 2,4) Output = 0 0 0 0 0 0 0 0

ones (5,2) instruction creates a vector of five rows and two columns

Output = 1 1

1 1

1 1

1 1

a = [ 1 2 3] b = [4 5 6]

o a.*b = [4 10 18]

8 if c= [2 2 2]

o b.*c results in [8 10 12]

15 DEPT OF ECE

plot (t, x)

If x = [6 7 8 9] t = [1 2 3 4] this instruction will display a figure window which indicates the plot

of x versus t

stem (t,x) :- This instruction will display a figure window as shown

Subplot: This function divides the figure window into rows and columns. Subplot (2 2 1)

divides the figure window into 2 rows and 2 columns 1 represent number of the figure

Subplot (3 1 2) divides the figure window into 3 rows and 1 column 2 represent number of the

figure

o convSyntax: w = conv(u,v) Description: w = conv(u,v) convolves vectors u and v. Algebraically,

convolution is the same operation as multiplying the polynomials whose coefficients are the

elements of u and v.

16 DEPT OF ECE

o dispSyntax: disp(X) Description: disp(X) displays an array, without printing the array name. If X

contains a text string, the string is displayed.Another way to display an array on the screen is to

type its name, but this prints a leading "X=," which is not always desirable.Note that disp does not

display empty arrays.

o xlabelSyntax: xlabel('string') Description: xlabel('string') labels the x-axis of the current axes.

o ylabelSyntax : ylabel('string')

Description: ylabel('string') labels the y-axis of the current axes.

o titleSyntax : title('string') Description: title('string') outputs the string at the top and in the center of

the current axes.

o grid on Syntax : grid on Description: grid on adds major grid lines to the current axes.

o FFT Discrete Fourier transform. FFT(X) is the discrete Fourier transform (DFT) of vector X. For

matrices, the FFT operation is applied to each column. For N-D arrays, the FFT operation operates

on the first non-singleton dimension. FFT(X,N) is the N-point FFT, padded with zeros if X has less

than N points and truncated if it has more.

o absAbsolute value. abs(X) is the absolute value of the elements of X. When X is complex, abs(X)

is the complex modulus (magnitude) of the elements of X.

o anglePhase angle. angle(H) returns the phase angles, in radians, of a matrix with complex

elements.

o interpResample data at a higher rate using lowpass interpolation. y = interp(x,L) resamples the

sequence in vector X at L times the original sample rate. The resulting resampled vector Y is L

times longer, Length(y) = L*Length(x).

o decimateResample data at a lower rate after lowpass filtering.

y = decimate(x,M) resample‟s the sequence in vector X at 1/M times the original sample rate. The

resulting resample vector Y is M times shorter, i.e., Length(Y) = Ceil(Length(x)/M). By default,

Decimate filters the data with an 8th order Chebyshev Type I lowpass filter with cutoff frequency

.8*(Fs/2)/R, before resampling.

17 DEPT OF ECE

EXPERIMENT No 1

SINUSOIDAL WAVEFORM / SIGNAL BASED ON RECURSIVE

DIFFERENCE EQUATION

1.1 AIM:

Program for generation of Sinusoidal waveform / signal based on Recursive Difference Equation

1.2 TOOLS REQUIRED:

1. Mat lab software

2. Personal computer

1.3 THEORY:

LTI systems are defined by an Nth-order linear constant-coefficient difference equationOften the

leading coefficient a0 = 1. Then the output y[n] can be computed recursively from

1.4 PROGRAM:

%% Clear Section

clc;

clear all;

close all;

%% Signal Frequency and Sampling Frequency

f_hz=input('enter the signal frequency in Hz= ');

fs=input('enter the sampling frequency of the signal= ');

f0=2*pi*f_hz/fs % Sampled Signal Frequency in Radians

%% Calculation of y(n) coefficients

a1=-2*sin(f0);

a2=1;

%% Calculation of x(n) coefficients

b1=sin(f0);

%% Initial values

xnm1=1;

ynm1=0;

N M

mkmnxbknya

0 0

][][

N

k

M

m

mkmnxbknyany

1 0

][][][

18 DEPT OF ECE

ynm2=0;

for n=1:200

y(n)=b1*xnm1-a1*ynm1-a2*ynm2; % Recursive Equation

ynm2=ynm1;

ynm1=y(n);

xnm1=0;

end

%% Plot of Signal and its Spectrum

subplot(2,1,1)

plot(1:length(y),y);

grid on

xlabel('Time in Seconds');

ylabel('Amplitude of the Signal');

title(['Sinusoidal Signal of frequency ', num2str(f_hz), ' Hz']);

Ak=2*abs(fft(y));%/length(y); % Finding Spectrum using FFT

f=(0:1:(length(y)-1)/2)*fs/length(y); % Indices to frequency in Hz to plot

subplot(2,1,2)

plot(f,Ak(1:(length(y)/2)));

grid on

xlabel('Frequency in Hz')

ylabel('Magnetude of the Spectrum');

title(['Spectrum at ', num2str(f_hz), ' Hz frequency']);

19 DEPT OF ECE

1.5 OUTPUT AND WAVEFORM:

1.6 INSERT GRAPH SHEET (NORMAL)

20 DEPT OF ECE

EXPERIMENT No 2

DFT AND IDFT OF A SEQUENCE

AIM: DFT and IDFT of a given sequence

TOOLS REQUIRED:

1. Mat lab software

2. Personal computer

THEORY:

In this program the Discrete Fourier Transform (DFT) of a sequence x[n] is generated by using

the formula,

N-1

X(k) = Σ x(n) e-2πjk / N

Where, X(k) DFT of sequence x[n]

n=0

N represents the sequence length and it is calculated by using the command „length‟. The DFT

of any sequence is the powerful computational tool for performing frequency analysis of

discrete-time signals.

PROGRAM: clc;

close all;

clear all;

xn=input('Enter the sequence x(n)'); %Get the sequence from user

ln=length(xn); %find the length of the sequence

xk=zeros(1,ln); %initilise an array of same size as that of input sequence

ixk=zeros(1,ln); %initilise an array of same size as that of input sequence

%code block to find the DFT of the sequence

%-----------------------------------------------------------

for k=0:ln-1

for n=0:ln-1

xk(k+1)=xk(k+1)+(xn(n+1)*exp((-i)*2*pi*k*n/ln));

end

end

%------------------------------------------------------------

21 DEPT OF ECE

%code block to plot the input sequence

%------------------------------------------------------------

t=0:ln-1;

subplot(311);

stem(t,xn);

ylabel ('Amplitude');

xlabel ('Time Index');

title('Input Sequence');

%---------------------------------------------------------------

magnitude=abs(xk); % Find the magnitudes of individual DFT points

%code block to plot the magnitude response

%------------------------------------------------------------

t=0:ln-1;

subplot(312);

stem(t,magnitude);


xlabel ('K');

title('Magnitude Response');

%------------------------------------------------------------

% Code block to find the IDFT of the sequence

%------------------------------------------------------------

for n=0:ln-1

for k=0:ln-1

ixk(n+1)=ixk(n+1)+(xk(k+1)*exp(i*2*pi*k*n/ln));

end

end

ixk=ixk/ln;

%------------------------------------------------------------

%code block to plot the input sequence

t=0:ln-1;

subplot(313);

stem(t,ixk);ylabel ('Amplitude');xlabel ('Time Index');title('IDFT sequence');

22 DEPT OF ECE

OUTPUT AND WAVEFORMS:

EMPTY SPACE FOR CALCULATIONS

INSERT GRAPH SHEET (NORMAL)

23 DEPT OF ECE

EXPERIMENT No 3

FREQUENCY RESPONSE

AIM: Program to find Frequency Response of a system given in Transfer Function

TOOLS REQUIRED:

Matlab software

Personal computer

PROGRAM: %% Clear section

clear all;

close all;

clc;

%% Defining numerator & denominator coefficients and normalized Frequency points

b=input('enter the coefficients of Numerator polynomial in descending order of Z = ');% [1 -0.9

0.81]

a=input('enter the coefficients of Denominator polynomial in descending order of Z = ');% [1 -

0.6 0.36]

N=input('enter the no. of normalized frequency points used for calculating frequency response

(ex. 256, 512, 1024 etc) = ');%512

%% Finding Frequency response

[h,w]=freqz(b,a,N);

%h=vector containing frequency response coefficients

%w=vector containing normalized frequency values distributed in the digital range from 0 to PI

radians

%% Calculating Phase of h

phase_h=(angle(h))/pi;

%% Calculating Magnitude of h

mag_h=abs(h);

%% Plot of Magnitude and Phase responses of Frequency response

%Magnitude response

subplot(2,1,1);

plot(w,mag_h);grid;

xlabel('Frequency in radians');

24 DEPT OF ECE

ylabel('Magnitude');


% Phase response

subplot(2,1,2);

plot(w,phase_h);grid;


ylabel('Phase in degrees');

title('Phase Response');

%% Magnitude Response in dB

figure(2)

subplot(2,1,1);

plot(w,20*log10(mag_h));grid


ylabel('Magnitude in dB');

title('Magnetude Response');

%% Pole-Zero diagram

figure(3)

zplane(b,a);

WAVEFORM:


INSERT GRAPH SHEET(NORMAL)

25 DEPT OF ECE

EXPERIMENT No 4

FFT (FAST FOURIER TRANSFORM)

AIM: FFT of a sequence using DIT-FFT method

TOOLS REQUIRED:

Mat lab software

Personal computer

THEORY:

The Fast Fourier Transform is useful to map the time-domain sequence into a continuous

function of a frequency variable. The FFT of a sequence {x(n)} of length N is given by a

complex-valued sequence X(k).

10;)()(

0

2

NkenxkX

M

k

n

nkj

The above equation is the mathematical representation of the DFT. As the number of

computations involved in transforming a N point time domain signal into its corresponding

frequency domain signal was found to be N2 complex multiplications, an alternative algorithm

involving lesser number of computations is opted.

When the sequence x(n) is divided into 2 sequences and the DFT performed separately, the

resulting number of computations would be N2/2(i.e.)

kn

N

N

n

N

n

nk

NWnxWnxkx

)12(12

0

12

0

2)12()2()(

2 2

Consider x (2n) be the even sample sequences and x (2n+1) be the odd sample sequence derived

formx(n).

12

0

2

2

)2(

N

n

nk

NWnx

would result in

26 DEPT OF ECE

(N/2)2multiplication‟s

12

0

)12(

2

)12(

N

n

kn

NWnx

Another (N/2)2

multiplication's finally resulting in (N/2)2 +

(N/2)2=

nsComputatioNNN

244

222

Further solving Eg.

k

N

nk

N

N

n

N

n

nk

NWWnxWnxkx

)2(12

0

12

0

2)12()2()(

2

)2(12

0

12

0

2)12()2(

nk

N

N

n

N

n

k

N

nk

NWnxWWnx

Dividing the sequence x(2n) into further 2 odd and even sequences would reduce the

computations.

WN is the twiddle factor

n

j

e

2

nkn

j

nk

NeW

2

22

NK

NN

NK

NWWW

2

22 n

n

j

kn

j

ee

27 DEPT OF ECE

kn

j

k

NeW

2

)sin(cos jW

k

N

)1(2

k

N

NK

NWW

k

N

NK

NWW

2

Employing this equation, we deduce

)2(12

0

12

0

2)12()2()(

2

nk

N

N

n

N

n

nk

NWnxWnxkx

)2(12

12

0

2)12()2()

2(

nk

N

N

N

n

K

N

nk

NWnxWWnx

Nkx

The time burden created by this large number of computations limits the usefulness of DFT in

many applications. Tremendous efforts devoted to develop more efficient ways of computing

DFT resulted in the above explained Fast Fourier Transform algorithm. This mathematical

shortcut reduces the number of calculations the DFT requires drastically. The above mentioned

radix-2 decimation in time FFT is employed for domain transformation.

Dividing the DFT into smaller DFTs is the basis of the FFT. A radix-2 FFT divides the DFT into

two smaller DFTs, each of which is divided into smaller DFTs and so on, resulting in a

combination of two-point DFTs. The Decimation -In-Time (DIT) FFT divides the input (time)

sequence into two groups, one of even samples and the other of odd samples. N/2 point DFT are

performed on the these sub-sequences and their outputs are combined to form the N point DFT.

28 DEPT OF ECE

Figure

The above shown mathematical representation forms the basis of N point FFT and is called the

butterfly structure

BUTTERFLY STRUCTURE.

STAGE – I

STAGE - II

29 DEPT OF ECE

STAGE – III

Figure: 8 POINT DIT

% Direct computation of FFT

x=[1 1 0 0];

N=4;

y=fft(x,N);

stem(abs(y));


xlabel ('N');


%Matlab Program for FFT using DIT algorithm

clc; clear all; close all;

x=input('enter x[n]:');

N=length(x);

levels=nextpow2(N);

xn=[x,zeros(1,(2^levels)-N)];

x=bitrevorder(xn)

N=length(xn);

tw=cos(2*pi*(1/N)*(0:N/2-1))-j*sin(2*pi*(1/N)*(0:N/2-1));

for level=1:levels;

L=2^level;

30 DEPT OF ECE

twlvl=tw(1:N/L:N/2);

for k=0:L:N-L;

for n=0:L/2-1;

A=x(n+k+1);

B=x(n+k+(L/2)+1)*twlvl(n+1);

x(n+k+1)=A+B;

x(n+k+(L/2)+1)=A-B;

end

end

x

end

XK=x

n=0:N-1;

subplot(2,2,1);stem(n,xn);title('x(n)');xlabel('n');ylabel('Amplitude');

subplot(2,2,2);stem(n,real(XK));title('Real part of X(K)');xlabel('n');ylabel('Amplitude');

subplot(2,2,3);stem(n,imag(XK));title('Imag part of X(K)');xlabel('n');ylabel('Amplitude');

OUTPUT AND WAVEFORM:

enter x[n]:[1 2 3 4 4 3 2 1]

XK =

20.0000 -5.8284 - 2.4142i 0 -0.1716 - 0.4142i 0 -0.1716 + 0.4142i

0 -5.8284 + 2.4142i

31 DEPT OF ECE



32 DEPT OF ECE

EXPERIMENT No 5

POWER SPECTRAL DENSITY

AIM:

Power spectral density

Tools Required:

Mat lab software

Personal computer

THEORY:

Power spectral density function (PSD) shows the strength of the variations (energy) as a function of

frequency. In other words, it shows at which frequencies variations are strong and at which frequencies

variations are weak. The unit of PSD is energy per frequency (width) and you can obtain energy within a

specific frequency range by integrating PSD within that frequency range. Computation of PSD is done

directly by the method called FFT or computing autocorrelation function and then transforming it.

PROGRAM:

clc;clearall;close all;

t = 0:0.001:0.6;

x =sin(2*pi*50*t)+sin(2*pi*120*t);

y = x + 2*randn(size(t));

figure,plot(1000*t(1:50),y(1:50)) ;

title('Signal Corrupted with Zero-Mean Random Noise');

xlabel('time (milliseconds)');

Y = fft(y,512);

%The power spectral density, a measurement of the energy at various frequencies, is:

Pyy = Y.* conj(Y) / 512;

f = 1000*(0:256)/512;

figure,plot(f,Pyy(1:257));

title('Frequency content of y');

xlabel('frequency (Hz)');

33 DEPT OF ECE

WAVEFORMS:



34 DEPT OF ECE

EXPERIMENT No 6&7

FIRLOWPASS AND HIGHPASSFILTER

AIM:

FIR low pass and high pass Filter design window techniques

TOOLS REQUIRED:

Mat lab software

Personal computer

ALGORITHM:-

1) Enter the pass band ripple (rp) and stop band ripple (rs).

2) Enter the pass band frequency (fp) and stop band frequency (fs).

3) Get the sampling frequency (f), beta value.

4) Calculate the analog pass band edge frequencies, wp and ws. wp = 2*fp/fws = 2*fs/f

5) Calculate the numerator and denominator

6)Use an if condition and ask the user to choose either Rectangular Window or Triangular

window or Kaiser window.

7) Use rectwin,triang,kaiser commands

8) Calculate the magnitude of the frequency response in decibels (dB m=20*log10(abs(h))

9) Plot the magnitude response [magnitude in dB Vs normalized frequency (o/pi)]

10)Give relevant names to x and y axes and give an appropriate title for the plot.

11)Plot all the responses in a single figure window.[Make use of subplot]

PROGRAM:

clc; clear all; close all;

rp=input('enter passband ripple');%0.02

rs=input('enter the stopband ripple'); %0.01

fp=input('enter passband freq'); %1000

fs=input('enter stopband freq');%1500

f=input('enter sampling freq '); %10000

beta=input('enter beta value'); %5

35 DEPT OF ECE

wp=2*fp/f; ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;

dem=14.6*((ws-wp)/(2*pi));

n=ceil(num/dem);

N=n+1;

c=input('enter your choice of window function 1. rectangular 2. triangular 3.kaiser: \n ');

if(c==1)

y=rectwin(N);

disp('Rectangular window filter response');

end

if (c==2)

y=triang(N);

disp('Triangular window filter response');

end

if(c==3)

y=kaiser(N,beta);

disp('kaiser window filter response');

end

%LPF

b=fir1(n,wp,'low',y);

[h,o]=freqz(b,1,256);

mag=20*log10(abs(h));

subplot(221);

semilogx(o/pi,mag); grid on;

title('magnitude response of FIR LPF');

ylabel('Gain in dB-->');

xlabel('Normalized frequency-->');

%HPF

b=fir1(n,wp,'high',y);

[h,o]=freqz(b,1,256);


36 DEPT OF ECE

subplot(222);


title('magnitude response of FIR HPF');



%BPF

wn=[wpws];

b=fir1(n,wn,y);

[h,o]=freqz(b,1,256);


subplot(223);


title('magnitude response of FIR BPF');



%BSF

b=fir1(n,wn,'stop',y);

[h,o]=freqz(b,1,256);


subplot(224);


title('magnitude response of FIR BSF');



37 DEPT OF ECE



INSERT GRAPH SHEET (SEMILOG)

38 DEPT OF ECE

EXPERIMENT No 8&9

IIR LOWPASS AND HIGHPASSFILTER

AIM:

IIR lowpass and highpass Filter design

TOOLS REQUIRED:

Mat lab software

Personal computer

THEORY:

The IIR filter can realize both the poles and zeroes of a system because it has a rational transfer

function, described by polynomials in z in both the numerator and the denominator:

N

k

k

k

M

k

k

k

Za

zb

zH

1

0)(

The difference equation for such a system is described by the following:

N

k

k

M

k

kknyaknxbny

10

)()()(

M and N are order of the two polynomialsbkand ak are the filter coefficients. These filter

coefficients are generated using FDS (Filter Design software or Digital Filter design package).

IIR filters can be expanded as infinite impulse response filters. In designing IIR filters, cutoff

frequencies of the filters should be mentioned. The order of the filter can be estimated using

butter worth polynomial. That‟s why the filters are named as butter worth filters. Filter

coefficients can be found and the response can be plotted.

ALGORITHM:-

1) Enter the pass band ripple (alphap) and stop band ripple (alphas).

2) Enter the pass band frequency (fp) and stop band frequency (fs).

3) Get the sampling frequency (F).

39 DEPT OF ECE

4) Calculate the analog pass band edge frequencies, omegap and omegas. omegap =

2*fp/Fomegas = 2*fs/F

5) Calculate the order and 3dB cutoff frequency of the analog filter. [Make use of the

following function] [n,wn]=buttord(omegap,omegas,rp,rs)

6) Design an nth order analog lowpass Butter worth filter using the following statement.

[b,a]=butter(n,wn, „low‟)

7) Find the complex frequency response of the filter by using freqz( ) function

[h,om]=freqz(b,a,w) where, w = 0:0.01:pi This function returns complex frequency

response vector „h‟ and frequency vector „om‟ in radians/samples of the filter.

8) Calculate the magnitude of the frequency response in decibels (dB

m=20*log10(abs(h))

9) Plot the magnitude response [magnitude in dB Vs normalized frequency (om/pi)]

10) Calculate the phase response using an = angle(h)

11) Plot the phase response [phase in radians Vs normalized frequency (om/pi)]

12) Give relevant names to x and y axes and give an appropriate title for the plot.

13) Plot all the responses in a single figure window.[Make use of subplot]

PROGRAM:

clc;clearall;close all;

disp('IIR filter design specifications:');

alpha

p=input('enter the passband attenuation:'); %0.15

alphas=input('enter the stopband attenuation:'); %60

fp=input('enter the passband frequency:'); % 1500

fs=input('enter the stopband frequency:'); % 3000

F=input('enter the sampling frequency:'); % 7000

omegap=2*fp/F;

omegas=2*fs/F;

%To find the cutoff frequency and order of the filter

[n,wn]=buttord(omegap,omegas,alphap,alphas);

%To find the system function of the lowpass filter

[b,a]=butter(n,wn,'low');%'high'

w=0:0.01:pi;

[h,om]=freqz(b,a,w);

40 DEPT OF ECE


an=angle(h);

figure(1);

subplot(211);plot(om/pi,mag);

title('magnitude response of IIR lowpass filter is:');

xlabel('normalized frequency');

ylabel('Gain in dB');

subplot(212);plot(om/pi,an);

title('phase response of IIR lowpass filter is:');


ylabel('Phase in radians');

%To find the system function of the highpass filter

[b,a]=butter(n,wn,'high');

w=0:0.01:pi;

[h,om]=freqz(b,a,w);


an=angle(h);

figure(2);

subplot(211);plot(om/pi,mag);

title('magnitude response of IIR highpass filter is:');


ylabel('Gain in dB');

subplot(212);plot(om/pi,an);

title('phase response of IIR highpass filter is:');


ylabel('Phase in radians');

41 DEPT OF ECE

OUTPUT:


INSERT GRAPH SHEET (SEMILOG)

42 DEPT OF ECE

EXPERIMENT No 10

SINUSOIDAL SIGNAL THROUGH FILTERING

AIM:

Program for generation of Sinusoidal Signal through filtering

TOOLS REQUIRED:

Mat lab software

Personal computer

PROGRAM:

%% Clear Section

clear all;closeall;clc;

%% Signal Frequency and Sampling frequency

f_hz=1000; % Signal frequency (Change this value and test)

fs=8000; % Sampling frequency (change this value and test)

f0=2*pi*f_hz/fs; % Sampled Signal Frequency in Radians

t=0:1/fs:1; % Time Vector for 1 Second duration

x=[1 zeros(1,length(t)) ] % Initializing the input sequence to zero

%% Calculation of numerator coefficients

b0=0;

b1=sin(f0);

%% Calculation of denominator coefficients

a0=1;

a1=-2*sin(f0);

a2=1;

b=[b0 b1]; % Numerator coefficients

a=[a0 a1 a2]; % Denominator coefficients

%% Filtering Operation

y=filter(b,a,x);

%% Plot of Signal and its Spectrum

subplot(2,1,1)

plot(t(1:200),y(1:200)); % Select only 200 points for clear plot

xlabel('Time in Seconds');

43 DEPT OF ECE

ylabel('Amplitude of the Signal');

title(['Sinusoidal Signal of frequency ', num2str(f_hz), ' Hz']);

% One Sided spectrum

Ak=2*abs(fft(y))/length(y); % Finding FFT

f=(0:1:length(y)/2)*fs/length(y); % Indices to frequencies in Hz for plotting

subplot(2,1,2)

plot(f,Ak(1:(length(y)+1)/2)); % Plot upto folding frequency

xlabel('Frequency in Hz')

ylabel('Magnetude of the Spectrum');

title(['Spectrum at ', num2str(f_hz), ' Hz frequency']);




44 DEPT OF ECE

EXPERIMENT No 11

DECIMATION BY FACTOR D

AIM:

Decimation by factor D

TOOLS REQUIRED:

Mat lab software

Personal computer

THEORY:

Sampling rate conversion (SRC) is a process of converting a discrete-time signal at a given rate

to a different rate. This technique is encountered in many application areas such as:

Digital Audio

Communications systems

Speech Processing

Antenna Systems

Radar Systems etc

Sampling rates may be changed upward or downward. Increasing the sampling rate is called

interpolation, and decreasing the sampling rate is called decimation. Reducing the sampling rate

by a factor of M is achieved by discarding every M-1 samples, or, equivalently keeping every

Mthsample. Increasing the sampling rate by a factor of L (interpolation by factor L) is achieved

by inserting L-1 zeros into the output stream after every sample from the input stream of

samples.

DECIMATOR:

To reduce the sampling rate by an integer factor M, assume a new sampling period the re-

sampled signal is

The system for performing this operation, called down-samplerDown-sampling generally results

in aliasing. Therefore, in order to prevent aliasing, x(n) should be filtered prior to down-

sampling with a low-pass filter that has a cutoff frequency The cascade of a low-pass filter with

a down-sampler illustrated below and is called decimator.

nMTxnMxnxcd

45 DEPT OF ECE

PROGRAM:

clc; close all; clear all;

D= input('enter Down-sampling factor : ');

N = input('enter number of samples :');

n = 0:N-1;

x = sin(2*pi*0.043*n) + sin(2*pi*0.031*n);

y = decimate(x,D,'fir');

subplot(2,1,1);

stem(n,x(1:N));


xlabel('Time index n');

ylabel('Amplitude');

subplot(2,1,2);

m = 0:(N/D)-1;

stem(m,y(1:(N/D)));

title('Output Sequence');



46 DEPT OF ECE




47 DEPT OF ECE

EXPERIMENT No 12

INTERPOLATION BY A FACTOR I

AIM:

Interpolation by a factor I

TOOLS REQUIRED:

Mat lab software

Personal computer

THEORY:

To increase the sampling rate by an integer factor L. If xa(t) is sampled with a sampling

frequency fs = 1/Ts, then to increase the sampling rate by an integer factor L, it is necessary to

extract the samples from x(n). The samples of xi(n) for values of n that are integer multiples of L

are easily extracted from x(n) as follows:

The system performing the operation is called up-sampler and is shown below:

After up-sampling, it is necessary to remove the frequency scaled images in xi(n), except those

that are at integer multiples of 2π. This is accomplished by filtering xi(n) with a low-pass filter

that has a cutoff frequency of π /L and a gain of L. In the time domain, the low-pass filter inter

polates between the samples at integer multiples of L as shown and is called interpolator.

PROGRAM:


I = input('Up-sampling factor = ');

N = input('enter number of samples :');

n = 0:N-1;

x = sin(2*pi*0.043*n) + sin(2*pi*0.031*n);

y = interp(x,I);

LnTxLnxnxci

//

48 DEPT OF ECE

subplot(2,1,1);

stem(n,x(1:N));




subplot(2,1,2);

m = 0:(N*I)-1;

stem(m,y(1:N*I));







49 DEPT OF ECE

EXPERIMENT No 13

SAMPLING RATE CONVERSION BY A FACTOR I/D

AIM:

Sampling rate conversion by a factor I/D

TOOLS REQUIRED:

Mat lab software

Personal computer

THEORY:

SRC by rational factor: SRC by L/M requires performing an interpolation to a sampling rate

which is divisible by both L and M. The final output is then achieved by decimating by a factor

of M. The need for a non-integer sampling rate conversion appears when the two systems

operating at different sampling rates have to be connected, or when there is a need to convert the

sampling rate of the recorded data into another sampling rate for further processing or

reproduction. Such applications are very common in telecommunications, digital audio,

multimedia and others.

An example is transferring data from compact disc (CD) system at a rate of 44.1 kHz to a digital

audio tape at 48 kHz. This can be achieved by increasing the data rate of the CD by a factor of

48/44.1, a non-integer. Illustration for sampling rate converter is:

If M>L, the resulting operation is a decimation process by a non-integer, and when M<L it is

interpolation. If M=1, the generalized system reduces to the simple integer interpolation and if

L=1 it reduces to integer decimation.

PROGRAM:


L = input('Enter Up-sampling factor :');

M = input('Enter Down-sampling factor :');

Lowpass

filter

Gain = L

Cutoff =

min(p/L,

p/M)

L M x

d[nx[n] x

e[n x

o[n

T T/L T/L TM/L

50 DEPT OF ECE

N = input('Enter number of samples :');

n = 0:N-1;

x = sin(2*pi*0.43*n) + sin(2*pi*0.31*n);

y = resample(x,L,M);

subplot(2,1,1); stem(n,x(1:N));

axis([0 29 -2.2 2.2]);


xlabel('Time index n'); ylabel('Amplitude');

subplot(2,1,2);

m = 0:(N*L/M)-1;

stem(m,y(1:N*L/M));

axis([0 (N*L/M)-1 -2.2 2.2]);


xlabel('Time index n'); ylabel('Amplitude');




51 DEPT OF ECE

EXPERIMENT No 14

IMPULSE RESPONSE

AIM:

Impulse Response of First order and Second order systems

TOOLS REQUIRED:

Mat lab software

Personal computer

PROGRAM:

clear all;close all; clc;

%y(n)+y(n-1)+0.9y(n-2)=x(n)+0.5x(n-1)+0.5x(n-2)

%a=input('enter the coefficients of denominator polynomial= ');

%b=input('enter the coefcients of numerator polynomial= ');

b=[1 1 0.9];

a=[1 0.5 0.5];

N=32; % length of input sequence

x=[1 zeros(1,N)]

y=filter(b,a,x)

subplot(2,1,1)

stem(1:length(x),x);

xlabel('Time');


title('Impulse Sequence');

subplot(2,1,2)

stem(1:length(y),y);

xlabel('Time');


title('Impulse Response Sequence');

52 DEPT OF ECE




53 DEPT OF ECE

EXPERIEMENTS

(Using DSP Kit)

INTRODUCTION TO DSP PROCESSORS

A signal can be defined as a function that conveys information, generally about the state or

behavior of a physical system. There are two basic types of signals viz Analog (continuous time

signals which are defined along a continuum of times) and Digital (discrete-time).

Remarkably, under reasonable constraints, a continuous time signal can be adequately

represented by samples, obtaining discrete time signals. Thus digital signal processing is an ideal

choice for anyone who needs the performance advantage of digital manipulation along with

today‟s analog reality.

Hence a processor which is designed to perform the special operations(digital manipulations) on

the digital signal within very less time can be called as a Digital signal processor. The difference

between a DSP processor, conventional microprocessor and a microcontroller are listed below.

Microprocessor: or General Purpose Processor such as Intel xx86 or Motorola 680xx

Family

Contains - only CPU

-No RAM

-No ROM

-No I/O ports

-No Timer

MICROCONTROLLER

Such as 8051 familyContains - CPU

- RAM

- ROM

-I/O ports

- Timer &

- Interrupt circuitry

Some Micro Controllers also contain A/D, D/A and Flash Memory

DSP PROCESSORS

Such as Texas instruments and Analog DevicesContains

- CPU

54 DEPT OF ECE

- RAM

- ROM

- I/O ports

- Timer

Optimized for

- fast arithmetic

- Extended precision

- Dual operand fetch

- Zero overhead loop

- Circular buffering

The basic features of a DSP Processor are

Feature Use

Fast-Multiply accumulate Most DSP algorithms, including filtering,

transforms, etc. are multiplication- intensive

Multiple – access memory architecture Many data-intensive DSP operations require

reading a program instruction and multiple data

items during each instruction cycle for best

performance

Specialized addressing modes Efficient handling of data arrays and first-in,

first-out buffers in memory

Specialized program control Efficient control of loops for many iterative

DSP algorithms. Fast interrupt handling for

frequent I/O operations.

On-chip peripherals and I/O interfaces On-chip peripherals like A/D converters allow

for small low cost system designs. Similarly

I/O interfaces tailored for common peripherals

allow clean interfaces to off-chip I/O devices.

A digital signal processor (DSP) is an integrated circuit designed for high-speed data

manipulations, and is used in audio, communications, image manipulation, and other data-

acquisition and data-control applications. The microprocessors used in personal computers are

optimized for tasks involving data movement and inequality testing. The typical applications

requiring such capabilities are word processing, database management, spread sheets, etc. When

55 DEPT OF ECE

it comes to mathematical computations the traditional microprocessor are deficient particularly

where real-time performance is required. Digital signal processors are microprocessors

optimized for basic mathematical calculations such as additions and multiplications.

FIXED VERSUS FLOATING POINT:

Digital Signal Processing can be divided into two categories, fixed point and floating point

which refer to the format used to store and manipulate numbers within the devices. Fixed point

DSPs usually represent each number with a minimum of 16 bits, although a different length can

be used. There are four common ways that these 216 i,e., 65,536 possible bit patterns can

represent a number. In unsigned integer, the stored number can take on any integer value from 0

to 65,535, signed integer uses two's complement to include negative numbers from -32,768 to

32,767. With unsigned fraction notation, the 65,536 levels are spread uniformly between 0 and 1

and the signed fraction format allows negative numbers, equally spaced between -1 and 1. The

floating point DSPs typically use a minimum of 32 bits to store each value. This results in many

more bit patterns than for fixed point, 232 i,e., 4,294,967,296 to be exact. All floating point

DSPs can also handle fixed point numbers, a necessity to implement counters, loops, and signals

coming from the ADC and going to the DAC. However, this doesn't mean that fixed point math

will be carried out as quickly as the floating point operations; it depends on the internal

architecture.

C VERSUS ASSEMBLY:

DSPs are programmed in the same languages as other scientific and engineering applications,

usually assembly or C. Programs written in assembly can execute faster, while programs written

in C are easier to develop and maintain. In traditional applications, such as programs run on PCs

and mainframes, C is almost always the first choice. If assembly is used at all, it is restricted to

short subroutines that must run with the utmost speed.

HOW FAST ARE DSPS?

The primary reason for using a DSP instead of a traditional microprocessor is speed: the ability

to move samples into the device and carry out the needed mathematical operations, and output

the processed data. The usual way of specifying the fastness of a DSP is: fixed point systems are

often quoted in MIPS (million integer operations per second). Likewise, floating point devices

can be specified in MFLOPS (million floating point operations per second).

56 DEPT OF ECE

TMS320 FAMILY:

The Texas Instruments TMS320 family of DSP devices covers a wide range, from a 16-bit fixed-

point device to a single-chip parallel-processor device. In the past, DSPs were used only in

specialized applications. Now they are in many mass-market consumer products that are

continuously entering new market segments. The Texas Instruments TMS320 family of DSP

devices and their typical applications are mentioned below.

C1x, C2x, C2xx, C5x, and C54x:

The width of the data bus on these devices is 16 bits. All have modified Harvard architectures.

They have been used in toys, hard disk drives, modems, cellular phones, and active car

suspensions.

C3x:

The width of the data bus in the C3x series is 32 bits. Because of the reasonable cost and

floating-point performance, these are suitable for many applications. These include almost any

filters, analyzers, hi-fi systems, voice-mail, imaging, bar-code readers, motor control, 3D

graphics, or scientific processing.

C4x:

This range is designed for parallel processing. The C4x devices have a 32-bit data bus and are

floating-point. They have an optimized on-chip communication channel, which enables a

number of them to be put together to form a parallel-processing cluster. The C4x range devices

have been used in virtual reality, image recognition, telecom routing, and parallel-processing

systems.

C6x:

The C6x devices feature Velocity, an advanced very long instruction word (VLIW) architecture

developed by Texas Instruments. Eight functional units, including two multipliersand six

arithmetic logic units (ALUs), provide 1600 MIPS of cost-effective performance. The C6x DSPs

are optimized for multi-channel, multifunction applications, including wireless base stations,

pooled modems, remote-access servers, digital subscriber loop systems, cable modems, and

multi-channel telephone systems.

57 DEPT OF ECE

INTRODUCTION TO TMS 320 C6713 DSK

The high–performanceboard features the TMS320C6713 floating-point DSP. Capable of

performing 1350 million floating point operations per second, the C6713 DSK the most

powerful DSK development board.

The DSK is USB port interfaced platform that allows to efficiently develop and test applications

for the C6713. With extensive host PC and target DSP software support, the DSK provides ease-

of-use and capabilities that are attractive to DSP engineers. The 6713 DSP Starter Kit (DSK) is a

low-cost platform which lets customers evaluate and develop applications for the Texas

Instruments C67X DSP family. The primary features of the DSK are:

1. 225 MHz TMS320C6713 Floating Point DSP

2. AIC23 Stereo Codec

3. Four Position User DIP Switch and Four User LEDs

4. On-board Flash and SDRAM

TI‟s Code Composer Studio development tools are bundled with the 6713DSK providing the user

with an industrial-strength integrated development environment for C and assembly

programming. Code Composer Studio communicates with the DSP using an on-board JTAG

emulator through a USB interface. The TMS320C6713 DSP is the heart of the system. It is a core

member of Texas Instruments‟ C64X line of fixed point DSPs whose distinguishing features are

58 DEPT OF ECE

an extremely high performance 225MHz VLIW DSP core and 256Kbytes of internal memory.

On-chip peripherals include a 32-bit external memory interface (EMIF) with integrated SDRAM

controller, 2 multi-channel buffered serial ports (McBSPs), two on-board timers and an enhanced

DMA controller (EDMA). The 6713 represents the high end of TI‟s C6700 floating point DSP

line both in terms of computational performance and on-chip resources.

The 6713 has a significant amount of internal memory so many applications will have all code

and data on-chip. External accesses are done through the EMIF which can connect to both

synchronous and asynchronous memories. The EMIF signals are also brought out to standard TI

expansion bus connectors so additional functionality can be added on daughter card modules.

DSPs are frequently used in audio processing applications so the DSK includes an on-board

codec called the AIC23. Codec stands for coder/decoder, the job of the AIC23 is to code analog

input samples into a digital format for the DSP to process, then decode data coming out of the

DSP to generate the processed analog output. Digital data is sent to and from the codec on

McBSP1.

TMS320C6713 DSK OVERVIEW BLOCK DIAGRAM

59 DEPT OF ECE

The DSK has 4 light emitting diodes (LEDs) and 4 DIP switches that allow users to interact with

programs through simple LED displays and user input on the switches. Many of the included

examples make use of these user interfaces Options.

The DSK implements the logic necessary to tie board components together in a programmable

logic device called a CPLD. In addition to random glue logic, the CPLD implements a set of 4

software programmable registers that can be used to access the on-board LEDs and DIP switches

as well as control the daughter card interface.

AIC23 Codec

The DSK uses a Texas Instruments AIC23 (part #TLV320AIC23) stereo codec for input and

output of audio signals. The codec samples analog signals on the microphone or line inputs and

converts them into digital data so it can be processed by the DSP. When the DSP is finished with

the data it uses the codec to convert the samples back into analog signals on the line and

headphone outputs so the user can hear the output.

The codec communicates using two serial channels, one to control the codec‟s internal

configuration registers and one to send and receive digital audio samples. McBSP0 is used as the

unidirectional control channel. It should be programmed to send a 16-bit control word to the

AIC23 in SPI format. The top 7 bits of the control word should specify the register to be modified

and the lower 9 should contain the register value. The control channel is only used when

60 DEPT OF ECE

configuring the codec, it is generally idle when audio data is being transmitted, McBSP1 is used

as the bi-directional data channel. All audio data flows through the data channel. Many data

formats are supported based on the three variables of sample width, clock signal source and serial

data format. The DSK examples generally use a 16-bit sample width with the codec in master

mode so it generates the frame sync and bit clocks at the correct sample rate without effort on the

DSP side. The preferred serial format is DSP mode which is designed specifically to operate with

the McBSP ports on TI DSPs.

DSK hardware installation

Shut down and power off the PC

Connect the supplied USB port cable to the board

Connect the other end of the cable to the USB port of PC

Plug the other end of the power cable into a power outlet

Plug the power cable into the board

The user LEDs should flash several times to indicate board is operational

When you connect your DSK through USB for the first time on a Windows

Loaded PC the new hardware found wizard will come up. So, Install the drivers (The CCS CD

contains the require drivers for C6713 DSK).

TROUBLESHOOTING DSK CONNECTIVITY

If Code Composer Studio IDE fails to configure your port correctly, perform the following

steps:Test the USB port by running DSK Port test from the start menu

61 DEPT OF ECE

Use Start->Programs->Texas Instruments->Code Composer Studio->Code Composer Studio

C6713 DSK Tools ->C6713 DSK Diagnostic Utilities

The below Screen will appear

Select 6713 DSK Diagnostic Utility Icon from Desktop, The Screen Look like as below

Select Start Option

Utility Program will test the board

After testing Diagnostic Status you will get PASS

62 DEPT OF ECE

INTRODUCTION TO CODE COMPOSER STUDIO

Code Composer is the DSP industry's first fully integrated development environment(IDE) with

DSP-specific functionality. With a familiar environment liked MS-based C+, Code Composer

lets you edit, build, debug, profile and manage projects from asingle unified environment. Other

unique features include graphical signal analysis, injection/extraction of data signals via file I/O,

multi-processor debugging, automated testing and customization via a C-interpretive scripting

language and much more.

CODE COMPOSER FEATURES INCLUDE:

IDE

Debug IDE

Advanced watch windows

Integrated editor

File I/O, Probe Points, and graphical algorithm scope probes

Advanced graphical signal analysis

Interactive profiling

Automated testing and customization via scripting

Visual project management system

Compile in the background while editing and debugging

Multi-processor debugging

Help on the target DSP

TO CREATE A SYSTEM CONFIGURATION USING A STANDARD

CONFIGURATION FILES:

STEP 1: Start CCS Setup by double clicking on the Setup CCS desktop icon.

STEP 2: Select Family ->c67xx

Platform->simulator

Endean‟s->little

STEP 3: Click the Import button (File->import) to import our selection (c67xx_sim.ccs)to the

System configuration currently being created in the CCS Setup window.

STEP 4: Click the Save and Quit button to save the configuration in the System Registry.

STEP 5: Click the Yes button to start the CCS IDE when we exit CCS Setup. The CCSSetup

Closes and the CCS IDE automatically opens using the configuration we justcreated.

63 DEPT OF ECE

PROCEDURE TO WORK ON CODE COMPOSER STUDIO

STEP 1: Creating a New Project

From the Project menu, choose New. In the Project Name field, type the name we want for our

project. Each project we create must have a unique name, and Click Finish. The CCS IDE

creates a project file called projectname.pjt. This file stores our project settings and references

the various files used by our project.

The Project Creation wizard window displays.

64 DEPT OF ECE

STEP 2: Creating a source file

Create a new source file using „File ->new ->source file „ pull down menu and save the source

file with .c extension in the current project name directory. Save as type: c/c++ source file (*.c*)

Path: C:\CCStudio_v3.1\ MyProjects\Project Name\

STEP 3:Add files to our project (source file\ library file\ linker file)

SOURCE FILE: Add the source file in the project using „Project->add files to project‟ pull

down menu. Files of type: c/c++ source file (*.c*)

Path: C:\CCStudio_v3.1\ My Projects\Project Name\filename‟s

LIBRARY FILE: Add the library file in the project using „Project->add files to project‟ pull

down menu. Files of type: Object and Library Files (*.o*,*.l*)

Path: C:\CCStudio_v3.1\ C6000\ cgtools\ lib \ rts6700.lib

65 DEPT OF ECE

LINKER FILE: Add the linker file in the project using „Project->add files to project‟ pull down menu. Files of type: Linker command Files (*.cmd*,*.lcf*)

Path: C:\CCStudio_v3.1\ tutorial\ dsk6713\ hello1 \ hello.cmd

STEP 4:Building and Running the Program (compile\ Build\ Load Program\ Run)

COMPILE: Compile the program using the „Project-compile‟ pull down menu or by clicking

the shortcut icon on the left side of program window.

BUILD: Build the program using the „Project-Build‟ pull down menu or by clicking the

shortcut icon on the left side of program window.

66 DEPT OF ECE

LOAD PROGRAM:Load the program in program memory of DSP chip using the„File-load

program‟ pull down menu.Files of type:(*.out*)

Path: C:\CCStudio_v3.1\ MyProjects\Project Name\ Debug\ Project

ame.out

RUN: Run the program using the „Debug->Run‟ pull down menu or by clicking

theshortcut icon on the left side of program window.

STEP 5:observe output using graph

Choose View->Graph-> Time/Frequency. In The Graph Property Dialog, Change The Graph

Title, Start Address, And Acquisition Buffer Size, Display Data Size, Dsp Data Type, Auto

Scale, And Maximum Y- Value Properties To The Values.

67 DEPT OF ECE

EXPERIMENT No 1

N-POINT DFT

AIM:

Computation of N-point DFT of a Sequence Using DSK Code composer studio

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord

Operating System – Windows XP

Software – CCStudio_v3.1

THEORY:

In this program the Discrete Fourier Transform (DFT) of a sequence x[n] is generated by using

the formula,

N-1

X (k) = Σ x(n) e-2πjk / N

Where, X(k) DFT of sequence x[n]

n=0

N represents the sequence length and it is calculated by using the command „length‟. The DFT

of any sequence is the powerful computational tool for performing frequency analysis of

discrete-time signals.

PROGRAM:

#include <stdio.h>

#include <math.h>

intN,k,n,i;

float pi=3.1416,sumre=0,sumim=0,out_real[8]={0.0},out_imag[8]={0.0};

int x[32];

void main(void)

{

printf("enter the length of the sequence\n");

scanf("%d",&N);

68 DEPT OF ECE

printf("\nenter the sequence\n");

for(i=0;i<N;i++)

scanf("%d",&x[i]);

for(k=0;k<N;k++)

{

sumre=0;

sumim=0;

for(n=0;n<N;n++)

{

sumre=sumre+x[n]*cos(2*pi*k*n/N);

sumim=sumim-x[n]*sin(2*pi*k*n/N);

}

out_real[k]=sumre;

out_imag[k]=sumim;

printf("DFT of the sequence:\n");

printf("x[%d]=\t%f\t+\t%fi\n",k,out_real[k],out_imag[k]);

}

}

PROCEDURE:

Open code composer studio, make sure the dsp kit is turned on.

Start a new project using „project-new „ pull down menu, save it in a separate

directory(d:11951a0xxx) with name dft.

Write the program and save it as dft.c

Add the source files dft.cto the project using „project->add files to project‟ pull down menu.

Add the linker command file hello.cmd.

(path: c:ccstudio_v3.1\tutorial\dsk6713\hello1\hello.cmd)

Add the run time support library file rts6700.lib.

(path: c:ccstudio_v3.1\c6000\cgtools\lib\rts6700.lib)

Compile the program using the „project-compile‟ pull down menu

Build the program using the „project-build‟ pull down menu

Load the program (dft.out) in program memory of dsp chip using the„file-load program‟ pull

down menu.

Debug-> run

69 DEPT OF ECE

To view output graphically select view ->graph ->time and frequency.


enter the length of the sequence

4

enter the sequence

1 2 3 4

DFT of the sequence:

x[0]= 10.000000 + 0.000000i


x[1]= -1.999963 + 2.000022i


x[2]= -2.000000 + 0.000059i


x[3]= -2.000108 + -1.999934i

Empty Space for Calculations

Insert Graph Sheet (Normal)

70 DEPT OF ECE

EXPERIMENT No 2

GENERATION OF SINE WAVE USING C6713 DSK

AIM:

To generate a real time sine wave using TMS320C6713 DSK

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



PROCEDURE:

1. Connect CRO to the LINE OUT socket.

2. Now switch ON the DSK and bring up Code Composer Studio on PC

3. Create a new project with name sinewave.pjt

4. From File menu->New->DSP/BIOS Configuration->Select dsk6713.cdb and save it as

“ sinewave.cdb”

5. Add sinewave.cdb to the current project

6. Create a new source file and save it as sinewave.c

7. Add the source file sinewave.c to the project

8. Add the library file “dsk6713bsl.lib” to the project

( Path: C:\CCStudio\C6000\dsk6713\lib\dsk6713bsl.lib)

9. Copy files “dsk6713.h” and “dsk6713_aic23.h” to the Project folder

(Path: C:\CCStudio_v3.1\C6000\dsk6713\include)

10. Build (F7) and load the program to the DSP Chip ( File->Load Program(.out file))

11. Run the program (F5)

12. Observe the waveform that appears on the CRO screen and ccstudio simulator.

71 DEPT OF ECE

%% matlab code to generate the sine values of the look table

n=1:48;

x=sin(2*pi*n*1000/48000);

x1=round(x*2^15);

// c program for generation of sine wave using c6713 DSK

#include "sinewavecfg.h"

#include "dsk6713.h"

#include "dsk6713_aic23.h"

short loop=0;

short gain=1;

Int16 outbuffer[256];

const short BUFFERLENGTH=256;

inti=0;

DSK6713_AIC23_Config

config={0x0017,0x0017,0x00d8,0x00d8,0x0011,0x0000,0x0000,0x0043,0x0081,0x0001};

Int16 sine_table[48]={4277,8481,12540,16384,19948,23170,25997,28378,30274,31651,32488,

32766,32488,31651,30274,28378,25997,23170,19948,16384,12540,8481,4277,0,-4277,-8481,

-12540,-16384,-19948,-23170,-25997,-28378,-30274,-31651,-32488,-32766,-32488,-31651,

-30274,-28378,-25997,-23170,-19948,-16384,-12540,-8481,-4277,0};

Uint32 fs=DSK6713_AIC23_FREQ_48KHZ;

void main()

{

DSK6713_AIC23_CodecHandle hCodec;

DSK6713_init();

hCodec=DSK6713_AIC23_openCodec(0, &config);

DSK6713_AIC23_setFreq(hCodec, fs);

while(1)

{

outbuffer[i]=sine_table[loop];

while(!DSK6713_AIC23_write(hCodec, sine_table[loop])*gain);

i++;

if(i==BUFFERLENGTH) i=0;

if(++loop>47) loop=0;

}}

72 DEPT OF ECE

WAVEFORM:

a) output from code composer studio

b) output from the CRO


73 DEPT OF ECE

EXPERIMENT No 3

FIR FILTER USING RECTANGULAR WINDOW (LOW PASS)

AIM:

To generate a real time fir filter through Rectangular window using TMS320C6713 DSK

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



PROCEDURE:

1. Connect CRO to the LINE OUT sockets.




“ firfliter.cdb”

5. Add firfilter.cdb to the current project

6. Create a new source file and save it as firfilter.c

7. Add the source file firfilter.c to the project


(Path: C:\CCStudio\C6000\dsk6713\lib\dsk6713bsl.lib)






74 DEPT OF ECE

// c program for generation of fir filter using c6713 DSK

#include "firfiltercfg.h"



#include "stdio.h"

Floatfilter_coeff[]={-0.020203,-0.016567,0.009656,0.027335,0.011411,-0.023194,-

0.033672,0.000000,0.043293,0.038657,-0.025105,-0.082004,-0.041842,0.115971,0.303048,

0.386435,0.303048,0.115971,-0.041842,-0.082004,-0.025105,0.038657,0.043293,0.000000,-

0.033672,-0.023194,0.011411,0.027335,0.009656,-0.016567,-0.020203};//FIR Low pass

Rectangular Filter pass band range 0-1500Hz



void main()

{


Uint32 l_input, r_input,l_output, r_output;

DSK6713_init();

hCodec = DSK6713_AIC23_openCodec(0, &config);

DSK6713_AIC23_setFreq(hCodec, 1);

while(1)

{

while(!DSK6713_AIC23_read(hCodec, &l_input));

while(!DSK6713_AIC23_read(hCodec, &r_input));

l_output=(Int16)FIR_FILTER(&filter_coeff ,l_input);

r_output=l_output;

while(!DSK6713_AIC23_write(hCodec, l_output));

while(!DSK6713_AIC23_write(hCodec, r_output));

}

DSK6713_AIC23_closeCodec(hCodec);

}

signed int FIR_FILTER(float * h, signed int x)

{

inti=0;

signed long output=0;

75 DEPT OF ECE

static short intin_buffer[100];

in_buffer[0] = x;

for(i=30;i>0;i--)

in_buffer[i] = in_buffer[i-1];

for(i=0;i<32;i++)

output = output + h[i] * in_buffer[i];

return(output);

}

WAVEFORM:

a) Waveforms of input and output from cro

b)Function generator (input signal frequency at 1 KHz)

76 DEPT OF ECE

c)C6713DSK

d)Function generator (input signal frequency at 1500Hz)

e) Waveforms of input and output from CRO (output signal attenuates)

d)Function generator (input signal frequency at 2000Hz)

77 DEPT OF ECE

a) Waveforms of input and output from CRO (output signal fully attenuated)


78 DEPT OF ECE

EXPERIMENT No 4

FIR FILTER USING KAISER WINDOW (HIGH PASS)

AIM:

To generate a real time fir filter through KaiserWindow using TMS320C6713 DSK

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



PROCEDURE:

1. Connect CRO to the LINE OUT sockets.




“firfliter_kaiser.cdb”


6. Create a new source file and save it as firfilter_kaiser.c

7. Add the source file firfilter_kaiser.c to the project





10. Build (F7) and load the program to the DSP Chip (File->Load Program (.out file))



79 DEPT OF ECE

// c program for generation of fir filter using c6713 DSK

#include "firfilter_kaisercfg.h"



#include "stdio.h"

float filter_coeff[]={0.000000,-0.000138,-0.000611,-0.001345,-0.001607, 0.000000, 0.004714,

0.012033,0.018287,0.016731,0.000000,-0.035687,-0.086763,-0.141588,-0.184011,0.800005, -

0.184011,-0.141588,-0.086763,-0.035687,0.000000,0.016731,0.018287,0.012033,0.004714, -

0.000000,-0.001607,-0.001345,-0.000611,-0.000138,0.000000};//FIR High pass Kaiser filter pass band

range 800Hz-3.5KHz

void main()

{



DSK6713_init();



while(1)

{



l_output=(Int16)FIR_FILTER(&filter_coeff ,l_input);

r_output=l_output;



}


}

signed int FIR_FILTER(float * h, signed int x)

{

inti=0;

signed long output=0;

static short intin_buffer[100];

in_buffer[0] = x;

80 DEPT OF ECE

for(i=30;i>0;i--)

in_buffer[i] = in_buffer[i-1];

for(i=0;i<32;i++)

output = output + h[i] * in_buffer[i];

//output = x;

return(output);

}

WAVEFORM:

a) Waveforms of input and output from CRO

b)function generator (input signal frequency at 500Hz)

c)C6713DSK

d)function generator (input signal frequency at 800Hz)

81 DEPT OF ECE

e) Waveforms of input and output from CRO

d)function generator (input signal frequency at 1.1kHz)

e) Waveforms of input and output from CRO


82 DEPT OF ECE

EXPERIMENT No 5

IIR FILTER USING BUTTERWORTH APPROXIMATION (LOW PASS)

AIM:

To generate a real time iir filter through Butterworth approximation using TMS320C6713 DSK

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



PROCEDURE:

1. Connect CRO to the LINE OUT socket.




“iirfliter.cdb”


6. Create a new source file and save it as iirfilter.c

7. Add the source file iirfilter.c to the project








83 DEPT OF ECE

// c program for generation of iir filter using c6713 DSK

#include "iirfiltercfg.h"



#include "stdio.h"

const signed intfilter_coeff [ ] = {15241,15241,15241,32761,10161,7877};

//IIR_BUTERWORTH_LP FILTER pass band range 0-8kHz



void main()

{



DSK6713_init();



while(1)

{



l_output=IIR_FILTER(&filter_coeff ,l_input);

r_output=l_output;



}


}

signed int IIR_FILTER(const signed int * h, signed int x1)

{

static signed int x[6] = {0,0,0,0,0,0};

static signed int y[6] = {0,0,0,0,0,0};

int temp=0;

temp = (short int)x1;

x[0] = (signed int) temp;

84 DEPT OF ECE

temp = ( (int)h[0] * x[0]);

temp += ( (int)h[1] * x[1]);

temp += ( (int)h[1] * x[1]);

temp += ( (int)h[2] * x[2]);

temp -= ( (int)h[4] * y[1]);

temp -= ( (int)h[4] * y[1]);

temp -= ( (int)h[5] * y[2]);

temp >>=15;

if ( temp > 32767 )

{

temp = 32767;

}

else if ( temp < -32767)

{

temp = -32767;

}

y[0] = temp;

y[2] = y[1];

y[1] = y[0];

x[2] = x[1];

x[1] = x[0];

return (temp<<2);

}

RESULT:

a) Waveforms of input and output from CRO

b)function generator (input signal frequency at 1KHz)

85 DEPT OF ECE

b) C6713DSK

c) function generator (input signal frequency at 8kHz)

d) Waveforms of input and output from CRO

e) function generator (input signal frequency at 10kHz)

g) Waveforms of input and output from CRO (output signal attenuated)

86 DEPT OF ECE


87 DEPT OF ECE

CONTENT BEYOND SYLLABI

88 DEPT OF ECE

EXPERIMENT No 1

LINEAR CONVOLUTION

AIM:

Verify the linear convolution operation Using DSK Code composer studio

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



THEORY:

Convolution is a formal mathematical operation, just as multiplication, addition, and integration.

Addition takes two numbers and produces a third number, while convolution takes two signals

and produces a third signal. Convolution is used in the mathematics of many fields, such as

probability and statistics. In linear systems, convolution is used to describe the relationship

between three signals of interest: the input signal, the impulse response, and the output signal.

10)()()(

1

0

Nnknhkxny

N

k

In this equation, x(k), h(n-k) and y(n) represent the input to and output from the system at time

n. Here we could see that one of the input is shifted in time by a value every time it is multiplied

with the other input signal. Linear Convolution is quite often used as a method of implementing

filters of various types.

PROGRAM:

// Linear convolution program in c language using ccstudio

#include<stdio.h>

int x[15],h[15],y[15];

main()

{

inti,j,m,n;

89 DEPT OF ECE

printf("\n enter the length of first sequence m:");

scanf("%d",&m);

printf("\n enter the length of second sequence n:");

scanf("%d",&n);

printf("enter values for i/p sequence x(n):\n");

for(i=0;i<m;i++)

scanf("%d",&x[i]);

printf("enter values for i/p sequence h(n): \n");

for(i=0;i<n; i++)

scanf("%d",&h[i]);

// padding of zeros

for(i=m;i<=m+n-1;i++)

x[i]=0;

for(i=n;i<=m+n-1;i++)

h[i]=0;

/* convolution operation */

for(i=0;i<m+n-1;i++)

{

y[i]=0;

for(j=0;j<=i;j++)

{

y[i]=y[i]+(x[j]*h[i-j]);

}

}

//displaying the o/p

for(i=0;i<m+n-1;i++)

printf("\n the value of output y[%d]=%d\t",i,y[i]);

}

PROCEDURE:

Open Code Composer Studio; make sure the DSP kit is turned on.

Start a new project using „Project-new „pull down menu, save it in a separate directory (D:

11951A0xxx) with name linear convolution.

Write the program and save it as linearconv.c

90 DEPT OF ECE

Add the source files linearconv.cto the project using „Project->add files to project‟ pull down

menu.


(Path: C:CCstudio_V3.1\tutorial\dsk6713\hello1\hello.cmd)


(Path: C:CCstudio_v3.1\c6000\cgtools\lib\rts6700.lib)

Compile the program using the „Project-compile‟ pull down menu

Build the program using the „Project-Build‟ pull down menu

Load the program (linearconv.out) in program memory of DSP chip using the „File-load

program‟ pull down menu.

Debug-> Run

To View output graphically Select view ->graph ->time and frequency.


Enter first sequence length m: 4

Enter second sequence length n: 3

Enter i/p sequence for x (n):

1 2 3 4

Enter i/p sequence for h (n):

2 3 1

Output (Linear Convolution) sequence is:

y[0]=2 y[1]=7 y[2]=13 y[3]=19 y[4]=15 y[5]=4

91 DEPT OF ECE



92 DEPT OF ECE

EXPERIMENT No 2

CIRCULAR CONVOLUTION

AIM:

Verify the circular convolution operation using dsk code composer studio

EQUIPMENTS:

TMS 320C6713 Kit.

RS232 Serial Cable

Power Cord



THEORY:

Circular convolution is another way of finding the convolution sum of two input signals. It

resembles the linear convolution, except that the sample values of one of the input signals is

folded and right shifted before the convolution sum is found. Also note that circular convolution

could also be found by taking the DFT of the two input signals and finding the product of the

two frequency domain signals. The Inverse DFT of the product would give the output of the

signal in the time domain which is the circular convolution output. The two input signals could

have been of varying sample lengths. But we take the DFT of higher point, which ever signals

levels to. For e.g. If one of the signals is of length 256 and the other spans 51 samples, then we

could only take 256 point DFT. So the output of IDFT would be containing 256 samples instead

of 306 samples, which follows N1+N2 – 1 where N1 & N2 are the lengths 256 and 51

respectively of the two inputs. Thus the output which should have been 306 samples long is

fitted into 256 samples. The 256 points end up being a distorted version of the correct signal.

This process is called circular convolution.

93 DEPT OF ECE

PROGRAM:

//program to implement circular convolution

#include<stdio.h>

intm,n,x[30],h[30],y[30],i,j, k,x2[30],a[30];

void main()

{

printf("\n Enter the length of the first sequence\n");

scanf("%d",&m);

printf("\n Enter the length of the second sequence\n");

scanf("%d",&n);

printf("\n Enter the first sequence\n");

for(i=0;i<m;i++)

scanf("%d",&x[i]);

printf("\n Enter the second sequence\n");

for(j=0;j<n;j++)

scanf("%d",&h[j]);

if(m-n!=0) /*If length of both sequences are not equal*/

{

if(m>n) /* Pad the smaller sequence with zero*/

{

for(i=n;i<m;i++)

94 DEPT OF ECE

h[i]=0;

n=m;

}

for(i=m;i<n;i++)

x[i]=0;

m=n;

}

y[0]=0;

a[0]=h[0];

for(j=1;j<n;j++) /*folding h(n) to h(-n)*/

a[j]=h[n-j];

/*Circular convolution*/

for(i=0;i<n;i++)

y[0]+=x[i]*a[i];

for(k=1;k<n;k++)

{

y[k]=0;

/*circular shift*/

for(j=1;j<n;j++)

x2[j]=a[j-1];

x2[0]=a[n-1];

for(i=0;i<n;i++)

{

a[i]=x2[i];

y[k]+=x[i]*x2[i];

}

}

//displaying the result

printf("\n The circular convolution is: \n");

for(i=0;i<n;i++)

printf("%d \t",y[i]);

}

95 DEPT OF ECE

PROCEDURE:

Open Code Composer Studio, make sure the DSP kit is turned on.

Start a new project using „Project-new „ pull down menu, save it in a separate

directory(D:11951A0xxx) with name circular convolution.

Write the program and save it as circularconv.c

Add the source files circularconv.cto the project using „Project->add files to project‟ pull

down menu.


(Path: C:CCstudio_V3.1\tutorial\dsk6713\hello1\hello.cmd)


(Path: C:CCstudio_v3.1\c6000\cgtools\lib\rts6700.lib)

Compile the program using the „Project-compile‟ pull down menu

Build the program using the „Project-Build‟ pull down menu

Load the program (circularconv.out) in program memory of DSP chip using the„File-load

program‟ pull down menu.

Debug-> Run

To View output graphically Select view ->graph ->time and frequency.


Enter the length of the first sequence 4

Enter the length of the second sequence 3 Enter the first sequence

1 2 3 4

Enter the second sequence 1 2 3

The circular convolution is

18 16 10 16

96 DEPT OF ECE



97 DEPT OF ECE

Annexure –I

VIVA QUESTIONS

GENERATION OF SINUSOIDAL SIGNAL QUESTIONS

1. What is the difference between sin & cos signals?

2. What is meant by signal?

3. What is the difference between time domain & frequency domain signal?

4. What is the difference between periodic & a periodic signal.

5. What is the difference between orthogonal and orthonormal signals?

6. What is the need for Fourier series & Fourier transform?

7. What is the difference between discrete & digital signals?

8. What is the difference between even signal & odd signal?

9. What is the difference between power signal & energy signal?

10. What is the difference between amplitude scaling & time scaling of a signal?

11. What is the difference between deterministic & random signal?

LINEAR CONVOLUTION QUESTIONS

1. What is the requirement for convolution?.

2. What is the difference between convolution & correlation?

3. What is meant by impulse response?

4. Is it possible to represent any discrete time signal in terms of impulses? If yes,

represent by using example.

5. Draw the h(2n-k) & h(n-2k) for the following sequenceh(n) = { 4 3 2 1} assume (i) k=

3 (ii) k =5.

6. Write the expressions for LTI system convolution formula & causal LTI

systemconvolution formula.

7. What us the length of linear convolution if length of input & impulse responsesare N1

& N2 respectively?

8. What is the difference between continuous and discrete convolution?

98 DEPT OF ECE

CIRCULAR CONVOLUTION QUESTIONS

1. Why we need circular convolution?

2. What is the difference between circular & linear convolution?

3. What is the length of output sequence after circular convolution if the lengths ofinput &

impulse responses are M1 & M2 respectively?

4. State the circular convolution property of DFT?

5. Where we required convolution property?

6. What does zero padding mean? Where we required this concept?

7. What is difference between linear shifting & circular shifting of signal? Show

withexample.

8. What is difference between linear & circular folding of signal? Show withexample.

9. What is the advantage with sectioned convolution?

FAST FOURIER TRANSFORM QUESTION

1. What is the difference between continuous time & discrete time Fourier transform?

2. What is the condition for convergence of Fourier transform?

3. What is the difference between discrete Time Fourier Transform (DTFT)& DFT?

4. What is the difference between Z transform & DFT?

5. State convolution property of the DFT? Where we could use the convolutionproperty?

6. State Parseval‟stheorem.

7. State correlation property of the DFT.?

8. What is the difference between radix 2 & radix4 FFT algorithms?

9. Why we need FFT?.

10. What is the difference between decimation in time (DIT FFT) & Decimation

infrequency(DIFFFT) algorithms?

11. What is meant by „in-place‟ computation in DIF & DIF algorithms?

12. Which properties are used in FFT to reduce no of computations?

FIR FILTER QUESTIONS

1. What are the advantages of FIR as compared to IIR?

2. How many types of FIR design methods are used in real time?.

3. What is meant by Gibbs Phenomenon? Where we found such type of effect in FIR

Filters?

99 DEPT OF ECE

4. What are the advantages& disadvantages of Rectangular window FIR filter as

Compared to remaining window techniques?

5. Which window technique having less peak amplitude of side lobe as compared toall?

6. What do you understand by linear phase responce?

7. To design all types of filters what would be the expected impulse response?

8. What are the properties of FIR filter?.

9. How the zeros in FIR filter is located?

10. What are the desirable characteristics of the window?

11. What are the specifications required to design filter

IIR FILTER QUESTIONS

1. What is meant by IIR filter?

2. What is the difference between recursive & non-recursive systems?

3. Write the difference equation for IIR system.

4. What are the mapping techniques in IIR filter design? Discuss the advantage

&disadvantages of them.

5. What are IIR analog filters? What are the advantages & disadvantages of them?

6. What is the disadvantage in impulse invariance method?

7. What does warping effect mean? Where we found this effect? How can weeliminate

warping effect?

8. Explain the pole mapping procedure of Impulse invariant & bilinear

transformationmethod.

9. For given same specification which difference we found in Butter worth &chebyshev

filter.

10. What is the difference between type I & type II chebyshev filters?.

11. Where the poles are located for Butter worth &chedbyshev filters?

12. What is meant by spectral transformation?

13. Why we need spectral transformation in IIR filter?

POWER SPECTRUM DENSITY QUESTION

1. What is the difference between correlation & auto correlation function?

2. What is the difference between PSD & ESD?

3. What is the unit for energy density spectrum?

100 DEPT OF ECE

4. What is the formula for PSD of a function?

5. “Same power density spectrum signals always have same magnitude &phase

spectrums” Is above statement true (or) False: Justify your answer.

6. If we know the impulse response of the system, the How can you find output

signalpower density from the input signal?

7. What is the unit for power density spectrum?

8. What is the relation between auto correlation & PSD of a function?

DSP PROCESSORS QUESTIONS

1. How many types of DSP processors are available in the market?

2. TMS 320C6X, „C‟ stands for what?

3. What are the features of TMS 320C6X processor?

4. What is meant by VLIW architecture? Why we required in DSP processor?

5. How many functional units are in TMS 320C6X DSP processor?

6. What is meant by Circular addressing mode how is it useful for DSP?

7. Which instruction is used to move 16 bit constant in to the upper bits of a register?

8. What is the difference between Von Neumann architecture & Harvardarchitecture?

9. Which architecture is used in DSP processor?

10. How many instructions can we execute per cycle in TMS320C6X DSP processor?

11. What are the applications for the TMS320 DSP‟s?

12. Which soft ware tool is required to compile and run the DSP assembly program?

13. What is the difference between full version Code composer studio &DSK CCS?

Documents

DIGITAL SIGNAL PROCESSING - iare.ac.in · PDF file1 DEPT OF ECE DIGITAL SIGNAL PROCESSING LAB MANUAL Subject Code: A60493 Regulations : R15 – JNTUH Class : III Year II Semester (ECE)