Minor Proj Report

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A

PROJECT REPORT

ON

SPEECH RECOGNITION

Submitted in partial fulfillment for of the award of

Bachelor of Technology

In

Electronics &Communications

By:

Hitesh Garg (0181312807)

Prateek Gupta (0571312807)

Rachit Kumar Gupta (0741312807)

Vandana Chauhan (0481312807)

Under the guidance of

Ms. Neha Gupta

Lecturer

Department of Electronics and Communications

Guru Premsukh Memorial College of Engineering

245, Budhpur Village, G.T Karnal Road, Delhi-36.

Guru Gobind Singh Indraprastha University, Delhi

2010-2011



MINOR PROJECT

ON

SPEECH RECOGNITION

Submitted by:







Certificate

This is to certify that the dissertation/ project report (course code)

entitled: SPEECH RECOGNITION : done by Mr. Hitesh Garg

(0181312807), Mr. Prateek Gupta (0571312807), Mr. Rachit

Kumar Gupta (0741312807), Ms. Vandana Chauhan

(0481312807) is an authentic work carried out by him/her at Guru

Premsukh Memorial College of Engineering under my guidance.

The matter embodied in this has not been submitted earlier for the

award of any degree or diploma to best of my Knowledge and belief.

Date:

(Ms. Neha Gupta)Lecturer



Acknowledgments

In the: Acknowledgments: page, the writer recognizes his

indebtedness for guidance and assistance of the thesis adviser and

other member of the faculty. Courtesy demands that he also recognize

specific contributions by other persons or institutions such as libraries

and research foundations. Acknowledgments should be expressed

simply, tastefully, and tactfully duly singed above the E-mail should

also be given at the end.







Abstract

Many voice recognition algorithms have been developed in past. We havereferenced Tor¶s Speech recognition algorithm to do speech recognition in

real time.

We have used the frequency variation in speech patterns to identify Individual¶s

voice to respective operation. The challenges faced were the detection of voice

patterns and compensating for the ambient noise for successful detection of

individuals. To deal with the limited memory and processing power, we had to

remove the redundancies in the speech pattern data; hence we developed

fingerprinting as a solution. The compensation for noise was done by accurate

approximation of the ambient noise and calculating for a threshold level based

on the same.

This fingerprint is compared with the stored fingerprint in the dictionary to

detect which word has been spoken. For comparison we use pseudo

Euclidean distance method. If the word is recognized, corresponding

control signal is generated for the respective device.

The algorithm used for recognition is simulated on MATLAB. The voice

signal is read into MATLAB using wavread command. To convert analogsignal to digital form we first sample, then quantize the signal. The

fingerprints are obtained by passing through the filters which are thencompared with the stored fingerprints to generate control signal.



Table of Contents



List of Tables



List of Figures



List of Symbols, Abbreviations and Nomenclature



INTRODUCTION

We all use remote controlled devices in our daily life. These remotes have

to be manually operated by the user. These devices usually use infraredcommunication for transmitting the control signal. Also these remotes can

be controlled by anyone.

For this we used speaker dependent voice recognition algorithm. By use of

this algorithm we can recognize which word has been spoken and

corresponding control signals are generated.Many voice recognition algorithms have been developed in past. We havereferenced Tor¶s Speech recognition algorithm to do speech recognition in

real time. This helped us to implement voice recognition algorithm on aMATLAB 6.0

In our project, the fingerprints of the word are stored in the header file-Dictionary.

Then speaker speaks into the microphone, which acts as a transducer toconvert voice signal into electrical signal.which is further passed through the analog todigital converter(ADC). ADC converts the incoming analog signal to digital signal.

The ADC¶s output is checked at the rate of 4 KHz and

passed through 10 filters after every 250 samples. Thus we get 16 pointsfrom each filter. This gives total 160 data points for each word. This iscalled as the fingerprint of the word.

This fingerprint is compared with the stored fingerprint in the dictionary to

detect which word has been spoken. For comparison we use pseudoEuclidean distance method. If the word is recognized, corresponding

control signal is generated for the respective operation.

The filters used are chebyshev 4th order filters. To implement 4 th order

filters we have cascaded two 2nd order filters whose coefficients are

obtained using MATLAB 6.0. We used chebyshev type 2 filters as they aremonotonic in passband and equiripple in stop band.

The algorithm used for recognition is simulated on MATLAB. The voice

signal is read into MATLAB using wavread command. To convert analog

signal to digital form we first sample, then quantize the signal. Thefingerprints are obtained by passing through the filters which are thencompared with the stored fingerprints to generate control signal.



Overview of Methodology

Fi B i bl di of speech recognition

The B sic algor ithm of our code was to check the ADC input at a rate of 4 KHz. If value of

the ADC is greater than the threshold value it is interpreted as the beginning of a half a

second long word. The sample word passes through 8 band pass f ilters and is conver ted into a

f ingerpr int. The words to be matched are stored as f ingerpr ints in a dictionary so that sampled

word f ingerpr ints can be compared against them later. Once a f ingerpr int is generated from asample word it is compared against the dictionary f ingerpr ints and using the modif ied

Euclidean distance calculation f inds the f ingerpr int in the dictionary that is the closest match.

Based on the word that matched the best the program sends a PWM signal to the car to

perform basic operations like lef t r ight go, stop, or reverse.

y Initi l Threshold Cal lation:

At star t up as par t of the initialization the program reads the ADC input using timercounter0

and accumulates its value 256 times. By interpreting the read in ADC value as a number between 1 to 1/256, in f i ed point, and accmulating 256 times. The average value of ADC

was calculated without doing a multi ply or divide. Three average values are taken each with a16.4msec delay between the samples. Af ter receiving three average values, the threshold

value is to be four times the value of the median number. The threshold value is useful todetect when a word has been spoken or not.

y Fingerprint Generation:

The program considers a word detected if a sample value from the ADC is greater than the

threshold value. Every sample of ADC is typecast to an int and stored in a dummy var iable



Ain. The Ain value passes through eight 4th

order Chebyshev band pass filters with a 40 dBstop band for 2000 samples (half a second) once a word has been detected. When a filter is

used its output is squared and that value is accumulated with the previous squares of the filter output. After 125 samples the accumulated value is stored as a data point in the fingerprint of

that word. The accumulator is then cleared and the process is begun again. After 2000

samples 16 points have been generated from each filter, thus every sampled word is divided

up into 16 parts. Our code is based around using 10 filters and since each one outputs 16data points every fingerprint is made up of 160 data points.



Body of Thesis

The Speech/Voice Recognition Method.The Speech/Voice Recognition method is similar to the template generation method. The

only difference is that the voice print is loaded to the Random Access memory of the

microcontroller and is compared with the templates available in the database. The appropriateaction is taken once a match is found.

Filter Implementation:

Figure 2Flowchart for Template Generation (160 point data)

We chose a 4th order Chebyshev filter with 40 dB stop band since it had very sharp transitions

after the cutoff frequency. We designed 10 filters a low pass with a cutoff of 200 Hz, a high

pass with a cutoff of 1.8 KHz, and eight band passes that each had a 200 Hz bandwidth and

were evenly distributed from 200Hz to 1.8 KHz.Thus we had band pass filters that went from

200-400 Hz, 400-600, 600 ± 800 and so on all the way to the filter that covered 1.6 Khz ± 1.8Khz. We designed our filters in this way because we felt that most of the important frequency

content in words was within the first 2 KHz since this usually contains the first and secondspeech formants, (resonant frequencies) This also allowed us to sample at 4 KHz and gave us

almost enough time to implement 10 filters. We thought we needed ten filters each withapproximately a 200 Hz bandwidth so that we would have enough frequency resolution to

properly identify words.Originally we had 5 filters that spanned from 0 ± 4 KHz and were

sampling at 8 KHz, but this scheme did not produce consistent word recognition.

In order to implement 4th order Chebyshev filters, we cascaded 2 second order IIR filters in

series to make 4 th order filter using Prof. Land's sample assembly code for 2 nd order IIR

filters. We generated 4th

order IIR filter coefficients using Matlab 6.0 as described in the math

section above. The coefficients though are floating point numbers and to convert them to

fixed point we multiply the numbers by 256 and round it off to nearest integer instead of

using the float2fix macro, which does not round .We needed to call all our filters at a rate of 4

KHz, the sampling frequency.



In order to make a fingerprint from a word we had to pass the ADC output through all thefilters faster than the ADC sample time of 250µs.We also modified our filters slightly, by

altering the gain coefficient, to have a maximum filter gain of 20 instead of 1. This wasdone to prevent the filter output from under flowing and going to zero when it was squared.

The output of the filter was squared in order to store the intensity of the sound rather than just

the amplitude .To reduce the time squaring the filter output took it was combined with the

filter function and also the accumulation of the previous squared filter outputs was also putinto assembly to reduce the cycle time .Nonetheless the reduction in cycle time was not

enough to implement all 10 filters, so we stopped calling the high pass filter .Later on the low

pass filter was removed because low frequency noise seemed to be interfering with the filter

output.

Fingerprint Comparison:

Once the fingerprints are created and stored in the dictionary when a word was spoken, it was

compared against the dictionary fingerprints. In order to do the comparison, we called a

lookup() function. The lookup() function did a pseudo Euclidean distance formula by

calculating the sum of the absolute value of the difference between each sample finger print a

finger print from the dictionary. The dictionary has multiple words in it and the lookup went

through all of them and picked the word with the smallest calculated number. We hadoriginally used the square of the correct Euclidean distance calculation, d = (pi ± qi) 2. We

had originally used English words, go, left, right, stop, and back, but many of these wordsseemed to be very similar in frequency as far as our algorithm was concerned.We then went

to vowels and had better success, but we still wanted to use words that were directions and sowe went to Hindi The set of words that we used were mostly orthogonal, but in Hindi left is

baiya, which sound very similar to daiya and so that could not be used. We had previouslyhad success with snapping so we used that for left.

Voice Sampling:

Human Voice consists of frequency components from 100-2000Hz .According

to the Nyquist µs sampling theorm,Sampling is the process of converting a signal (for

example, a function of continuous time or space) into a numeric sequence (a function of

discrete time or space). The theorem states, in the original words of Shannon (where he uses

"cps" for "cycles per second" instead of the modern unit hertz): If a function f(t) contains no

frequencies higher than W cps, it is completely determined by giving its ordinates at a series

of points spaced 1/(2W) seconds apart.

Hence we need sampling at the rate of at least 4000Hz . Hence the sampling time should be

ideally 1/4000sec = 250s.

The voice sampling is achieved by setting the ADC control registers and a timer

which interrupts (triggers) the microcontroller to generate ADC data every

232s.

The method for sampling consists of the following steps:� Setup the interrupt for Counter 0 and Counter 1.

� Initializing the ADC data available flag to 0.� Configure the ADMUX register to obtain data from ADC channel 1.

� Setup the timer to interrupt the microcontroller to acquire data from ADC, every 232s.� Receive the ADC data into the Accumulator

� Process the data further as per the Voiceprint generation process.



Algorithm :

1. Set TIMSK watchdog timer control register to 0b00000010 so that it interrupts every time

the timer hits the count.

2. Set the ADC input data register to zero.

3. Set the ADMUX value to 0b00100000 to select channel 1.

4. ADCSR value is set to 0b11000111 to start the conversion and sets the ADC conversion

status flag to1.

5. The timer control register TCCR0=0b00001011 and OCR0=62 so that we get a sampling

rate of 4300Hz.

Bandpass Filtering:

The filter used here is Chebyshev Filter (IIR).

Infinite impulse response (IIR) is a property of signal processing systems.

Systems with that property are known as IIR systems or when dealing withelectronic filter systems as IIR filters. They have an impulse response function

which is non-zero over an infinite length of time. This is in contrast to finite

impulse response filters (FIR) which have fixed-duration impulse responses.

The simplest analog IIR filter is an RC filter made up of a single resistor (R)

feeding into a node shared with a single capacitor (C). This filter has an

exponential impulse response characterized by an RC time constant.

IIR filters may be implemented as either analog or digital filters. In digital IIR

filters, the output feedback is immediately apparent in the equations defining the

output. Note that unlike with FIR filters, in designing IIR filters it is necessary

to carefully consider "time zero" case in which the outputs of the filter have not

yet been clearly defined.

Design of digital IIR filters is heavily dependent on that of their analogcounterparts because there are plenty of resources, works and straightforwarddesign methods concerning analog feedback filter design while there are hardly

any for digital IIR filters. As a result, mostly, if a digital IIR filter is going to beimplemented, first, an analog filter (e.g. Chebyshev filter, Butterworth filter,

Elliptic filter) is designed and then it is converted to digital by applyingdiscretization techniques such as Bilinear transform or Impulse invariance.

Example IIR filters include the Chebyshev filter, Butterworth filter, and theBessel filter.

Bandpass Filter Design:

This is an important part for generating a voice template for the voice. This stepremoves the redundancies in voice and stores the signature in a 160 point vector

data.

The bandpass filter is a Second order Chebychev IIR filter. The coefficients for

the filter are calculated using MATLAB 6.0.

In order to analyze speech, we needed to look at the frequency content of the

detected word. To do this we used several 4th order Chebyshev band pass



filters. To create 4th order filters, we cascaded two second order filters using thefollowing "Direct Form II Transposed" implementation of a difference

equations.

Figure 3TransposedDirectFormII implementation of a second order IIR digital filter (input on the right, output on the left)

The filter expressions can be now written as.

The assembly language code is then written to implement the filter is written

taking care that the filter is able to calculate within 2100 system cycles that is before the next sample arrives. Hence to optimize the following process we

have optimized the data format from float to fixed point 2¶s complement form which hasimproves the performance of the program and helps to compute within the required number

of system clock cycles.

Filter Coefficient Calculation.

The filter coefficient is calculated using the Signal Processing Blockset of

MATLAB 6.0. The parameters for the bandpass filters are 100-200Hz,200-400Hz to 1800-

2000Hz(for 8 bandpass filters). The gain for the passband is 20dB and the rolloff is quite

steep as two IInd Order Chebyshev bandpass filter are cascaded in series



Matlab Function Description

cheby2 - Chebyshev Type II filter design (stopband ripple)

Syntax

[z,p,k]=cheby2(n,R,Wst)

[z,p,k]=cheby2(n,R,Wst,' ftype')

[b,a]=cheby2(n,R,Wst)[ b,a]=cheby2(n,R,Wst,' ftype')

[A,B,C,D]=cheby2(n,R,Wst)

[A,B,C,D]=cheby2(n,R,Wst,' ftype')[z,p,k]=cheby2(n,R,Wst,'s')

[z,p,k]=cheby2(n,R,Wst,'ftype' ,'s')[ b,a]=cheby2(n,R,Wst,'s')

[ b,a]=cheby2(n,R,Wst,'ftype' ,'s')[A,B,C,D]=cheby2(n,R,Wst,'s')

[A,B,C,D]=cheby2(n,R,Wst, 'ftype' ,'s')

Description

cheby2 designs lowpass, highpass, bandpass, and bandstop digital and analog ChebyshevType II filters. Chebyshev Type II filters are monotonic in the passband and equiripple in the

stopband. Type II filters do not roll off as fast as type I filters, but are free of passband ripple.

Digital Domain

[z,p,k] = cheby2(n,R,Wst) designs an order n lowpass digital Chebyshev Type II filter with normalized stopband edge frequency Wst and stopband ripple R dB down from the peak

passband value. It returns the zeros and poles in length n column vectors z and p and the gain

in the scalar k.

Normalized st o pband edge frequency is the beginning of the stopband, where the magnitude

response of the filter is equal to -R dB. For cheby2, the normalized stopband edge frequency

Wst is a number between 0 and 1, where 1 corresponds to half the sample rate. Larger values

of stopband attenuation R lead to wider transition widths (shallower rolloff characteristics).

If Wst is a two-element vector, Wst = [w1 w2], cheby2 returns an order 2*n bandpass filter

with passband w1 < < w2.

[z,p,k] = cheby2(n,R,Wst,'ftype')designs a highpass, lowpass, or bandstop filter,

where the string 'ftype' is one of the following:

y 'high' for a highpass digital filter with normalized stopband edge frequency Wst

y 'low' for a lowpass digital filter with normalized stopband edge frequency Wst

y 'stop' for an order 2*n bandstop digital filter if Wst is a two-element vector,

Wst = [w1 w2]. The stopband is w1 < < w2.



With different numbers of output arguments, cheby2 directly obtains other realizations of thefilter. To obtain the transfer function form, use two output arguments as shown below.

[b,a] = cheby2(n,R,Wst) designs an order n lowpass digital Chebyshev Type II filter with

normalized stopband edge frequency Wst and stopband ripple R dB down from the peak

passband value. It returns the filter coefficients in the length n+1 row vectors b and a, with

coefficients in descending powers of z.

[b,a] = cheby2(n,R,Wst,'ftype') designs a highpass, lowpass, or bandstop filter, where

the string 'ftype' is 'high', 'low', or 'stop', as described above.

To obtain state-space form, use four output arguments as shown below.

[A,B,C,D] = cheby2(n,R,Wst) or

[A,B,C,D] = cheby2(n,R,Wst,'ftype') where A, B, C, and D are

and u is the input, x is the state vector, and y is the output.

tf2sos - Convert digital filter transfer function data to second-order

sections form

Syntax

[sos,g]=tf2sos(b,a)

[sos,g] = tf2sos(b,a,'ord er')

[sos,g]=tf2sos(b,a, 'ord er','scale')

sos=tf2sos(...)

Description

tf2sos converts a transfer function representation of a given digital filter to an equivalent

second-order section representation.

[sos,g] = tf2sos(b,a) finds a matrix sos in second-order section form with gain g that isequivalent to the digital filter represented by transfer function coefficient vectors a and b.



sos is an L-by-6 matrix

whose rows contain the numerator and denominator coefficients bik and aik of the second-

order sections of H ( z).

[sos,g] = tf2sos(b,a,'ord er') specifies the order of the rows in sos, where 'ord er' is

y 'down', to order the sections so the first row of sos contains the poles closest to the

unit circle

y 'up', to order the sections so the first row of sos contains the poles farthest from theunit circle (default)

[sos,g] = tf2sos(b,a,'ord er','scale') specifies the desired scaling of the gain and

numerator coefficients of all second-order sections, where 'scale' is:

y 'none', to apply no scaling (default)

y 'inf', to apply infinity-norm scaling

y 'two', to apply 2-norm scaling

Using infinity-norm scaling in conjunction with up-ordering minimizes the probability of

overflow in the realization. Using 2-norm scaling in conjunction with down-orderingminimizes the peak round-off noise.

sos = tf2sos(...) embeds the overall system gain, g, in the first section, H 1( z), so that

sos2tf - Convert digital filter second-order section data to transfer

function form

Syntax

[ b,a]=sos2tf(sos)

[b,a] = sos2tf(sos,g)



Description

sos2tf converts a second-order section representation of a given digital filter to an

equivalent transfer function representation.

[b,a] = sos2tf(sos) returns the numerator coefficients b and denominator coefficients a

of the transfer function that describes a discrete-time system given by sos in second-order section form. The second-order section format of H ( z) is given by

sos is an L- by-6 matrix that contains the coefficients of each second-order section stored inits rows.

Row vectors b and a contain the numerator and denominator coefficients of H ( z) stored indescending powers of z.

[b,a] = sos2tf(sos,g) returns the transfer function that describes a discrete-time system

given bysos

in second-order section form with gaing

.

.

freqz - Frequency response of digital filter

Syntax

[h,w]=freqz(b,a,n)h=freqz(b,a,w)

[h,w]=freqz(b,a,n,'whole')[h,f]=freqz(b,a,n,fs)

h=freqz(b,a,f,fs)

[h,f]=freqz(b,a,n,'whole',fs)

freqz(b,a,...) freqz(Hd)



Description

[h,w] = freqz(b,a,n) returns the frequency response vector h and the corresponding

angular frequency vector w for the digital filter whose transfer function is determined by the

(real or complex) numerator and denominator polynomials represented in the vectors b and a,

respectively. The vectors h and w are both of length n. The angular frequency vector w has

values ranging from 0 to radians per sample. If you do not specify the integer n, or you

specify it as the empty vector [], the frequency response is calculated using the default valueof 512 samples.

h = freqz(b,a,w) returns the frequency response vector h calculated at the frequencies (in

radians per sample) supplied by the vector w. The vector w can have any length.

[h,w] = freqz(b,a,n,'whole') uses n sample points around the entire unit circle to

calculate the frequency response. The frequency vector w has length n and has values ranging

from 0 to 2 radians per sample.

[h,f] = freqz(b,a,n,fs) returns the frequency response vector h and the correspondingfrequency vector f for the digital filter whose transfer function is determined by the (real or

complex) numerator and denominator polynomials represented in the vectors b and a,

respectively. The vectors h and f are both of length n. For this syntax, the frequency response

is calculated using the sampling frequency specified by the scalar fs (in hertz). The

frequency vector f is calculated in units of hertz (Hz). The frequency vector f has values

ranging from 0 to fs/2 Hz.

h = freqz(b,a,f,fs) returns the frequency response vector h calculated at the frequencies

(in Hz) supplied in the vector f. The vector f can be any length.

[h,f] = freqz(b,a,n,'whole',fs) uses n points around the entire unit circle to calculate

the frequency response. The frequency vector f has length n and has values ranging from 0 tofs Hz.

freqz(b,a,...) plots the magnitude and unwrapped phase of the frequency response

of the filter. The plot is displayed in the current figure window.

freqz(Hd) plots the magnitude and unwrapped phase of the frequency response of the filter.

The plot is displayed in fvtool. The input Hd is a dfilt filter object or an array of dfilt

filter objects.

reshape - Reshape arraySyntax

B = reshape(A,m,n) B = reshape(A,m,n,p,...)

B = reshape(A,[m n p ...])B = reshape(A,...,[],...)

B = reshape(A,siz)



Description

B = reshape(A,m,n) returns the m -by-n matrix B whose elements are taken column-wise

from A . An error results if A does not have m*n elements.

B = reshape(A,m,n,p,...) or B = reshape(A,[m n p ...]) returns an n-dimensional

array with the same elements as A but reshaped to have the size m-by-n-by-p-by-.... The product of the specified dimensions, m*n*p*..., must be the same as prod(size(A)).

B = reshape(A,...,[],...) calculates the length of the dimension represented by the

placeholder [], such that the product of the dimensions equals prod(size(A)) . The value of

prod(size(A)) must be evenly divisible by the product of the specified dimensions. You can

use only one occurrence of [].

B = reshape(A,siz) returns an n-dimensional array with the same elements as A, but

reshaped to siz, a vector representing the dimensions of the reshaped array. The quantity

prod(siz) must be the same as prod(size(A)) .

wavread - Read WAVE (.wav) sound file

Graphical Interface

As an alternative to wavread, use the Import Wizard. To activate the Import Wizard, select

File > Import Data.

Syntax

y = wavread( filename)

[ y, Fs] = wavread( filename)[ y, Fs, nbits] = wavread( filename) [ y, Fs, nbits, o pts] = wavread( filename)

[...] = wavread( filename, N )[...] = wavread( filename, [ N 1 N2])

[...] = wavread(..., fmt )

siz = wavread( filename,'size')

Description

y = wavread(filenam e) loads a WAVE file specified by the string filenam e, returning the

sampled data in y . If filenam e does not include an extension, wavread appends .wav.

[y , F s] = wavread(filenam e) returns the sample rate (F s) in Hertz used to encode the

data in the file.

[ y , Fs, nbits] = wavread(filename) returns the number of bits per sample (nbits).

[y , F s, nbits, o pts] = wavread(filenam e) returns a structure o pts of additional

information contained in the WAV file. The content of this structure differs from file to file.



Typical structure fields include o pts.fmt (audio format information) and o pts.info (textthat describes the title, author, etc.).

[...] = wavread(filenam e, N ) returns only the first N samples from each channel in the

file.

[...] = wavread(filenam e, [N1 N2]) returns only samples N1 through N2 from eachchannel in the file.

[...] = wavread(..., f m t) specifies the data format of y used to represent samples read

from the file. f m t can be either of the following values, or a partial match (case-insensitive):

'double' Double-precision normalized samples (default).

'native' Samples in the native data type found in the file.

siz = wavread(filenam e,'size') returns the size of the audio data contained in

filenam e instead of the actual audio data, returning the vector siz = [sam ples channels].

wavread supports multi-channel data, with up to 32 bits per sample.

wavread supports Pulse-code Modulation (PCM) data format only.

mean - Average or mean value of array

Syntax

M = mean(A)

M = mean(A,dim)

Description

M = mean(A) returns the mean values of the elements along different dimensions of an array.

If A is a vector, mean(A) returns the mean value of A.

If A is a matrix, mean(A) treats the columns of A as vectors, returning a row vector of mean

values.

If A is a multidimensional array, mean(A) treats the values along the first non-singleton

dimension as vectors, returning an array of mean values.

M = mean(A,dim) returns the mean values for elements along the dimension of A specified

by scalar dim. For matrices, mean(A,2) is a column vector containing the mean value of eachrow.



decimate - Decimation decrease sampling rate

Syntax

y=decimate(x,r) y=decimate(x,r,n)

y=decimate(x,r,'fir')y=decimate(x,r,n,'fir')

Description

Decimation reduces the original sampling rate for a sequence to a lower rate, the opposite of

interpolation. The decimation process filters the input data with a lowpass filter and thenresamples the resulting smoothed signal at a lower rate.

y = decimate(x,r) reduces the sample rate of x by a factor r. The decimated vector y is r

times shorter in length than the input vector x. By default, decimate employs an eighth-order

lowpass Chebyshev Type I filter with a cutoff frequency of 0.8*(Fs/2)/r. It filters the input

sequence in both the forward and reverse directions to remove all phase distortion, effectively

doubling the filter order.

y = decimate(x,r,n) uses an order n Chebyshev filter. Orders above 13 are not

recommended because of numerical instability. In this case, a warning is displayed.

y = decimate(x,r,'fir') uses an order 30 FIR filter, instead of the Chebyshev IIR filter.

Here decimate filters the input sequence in only one direction. This technique conserves

memory and is useful for working with long sequences.

y = decimate(x,r,n,'fir') uses an order n FIR filter.

abs - Absolute value and complex magnitude

Syntax

abs(X)

Description

abs(X) returns an array Y such that each element of Y is the absolute value of the

corresponding element of X.

If X is complex, abs(X) returns the complex modulus (magnitude), which is the same as

sqrt(real(X).^2 + imag(X).^2)



1-D digital filter

Syntax

y = filter(b,a,X) [y,zf] = filter(b,a,X)

[y,zf] = filter(b,a,X,zi)y = filter(b,a,X,zi,dim)

[...] = filter(b,a,X,[],dim)

Description

The filter function filters a data sequence using a digital filter which works for both real

and complex inputs. The filter is a direct f orm II transpo sed implementation of the standard

difference equation.

y = filter(b,a,X) filters the data in vector X with the filter described by numerator

coefficient vector b and denominator coefficient vector a. If a(1) is not equal to 1, filter

normalizes the filter coefficients by a(1). If a(1) equals 0, filter returns an error.

If X is a matrix, filter operates on the columns of X. If X is a multidimensional array,

filter operates on the first nonsingleton dimension.

[y,zf] = filter(b,a,X) returns the final conditions, zf, of the filter delays. If X is a row

or column vector, output zf is a column vector of max(length(a),length(b)) -1. If X is a

matrix, zf is an array of such vectors, one for each column of X, and similarly for multidimensional arrays.

[y,zf] = filter(b,a,X,zi) accepts initial conditions, zi, and returns the final conditions,

zf, of the filter delays. Input zi is a vector of length max(length(a),length(b)) -1, or anarray with the leading dimension of size max(length(a),length(b)) -1 and with remaining

dimensions matching those of X.

y = filter(b,a,X,zi,dim) and [...] = filter(b,a,X,[],dim) operate across the

dimension dim.

sum - Sum of array elements

Syntax

B = sum(A) B = sum(A,dim)

B = sum(..., 'double')

B = sum(..., dim,'double')

B = sum(..., 'native')

B = sum(..., dim,'native')



Description

B = sum(A) returns sums along different dimensions of an array. If A is floating point, that is

double or single, B is accumulated natively, that is in the same class as A, and B has the same

class as A. If A is not floating point, B is accumulated in double and B has class double.

If A is a vector, sum(A) returns the sum of the elements.

If A is a matrix, sum(A) treats the columns of A as vectors, returning a row vector of the sums

of each column.

If A is a multidimensional array, sum(A) treats the values along the first non-singletondimension as vectors, returning an array of row vectors.

B = sum(A,dim) sums along the dimension of A specified by scalar dim. The dim input is an

integer value from 1 to N, where N is the number of dimensions in A. Set dim to 1 to computethe sum of each column, 2 to sum rows, etc.

B = sum(..., 'double') and B = sum(..., dim,'double') performs additions in

double-precision and return an answer of type double, even if A has data type single or aninteger data type. This is the default for integer data types.

B = sum(..., 'native') and B = sum(..., dim,'native') performs additions in the

native data type of A and return an answer of the same data type. This is the default for

single and double.

If A = int8(1:20) then sum(A) accumulates in double and the result is double(210) while

sum(A,'native') accumulates in int8, but overflows and saturates to int8(127) .

Documents

Minor Proj Report