Basics About Signals Systems

Presentation by:

Mr. S. Karthie,

Assistant Professor/ECE

SSN College of Engineering

CS2403 - Digital Signal Processing

OUTLINE OF THIS COURSE�Introduction – Basics of Signals & Systems (Unit-I)

�Discrete Time LTI Systems – Analysis (Unit-I)

�Z-Transform (Unit-I)

�Discrete Fourier Transform & Fast Fourier Transform (Unit-II)

�Digital Filter Structures

�IIR Filter Design (Unit-III)

�FIR Filter Design (Unit-IV)

�Finite Word length Effects (Unit-IV)

�Applications of DSP (Unit-V)

Introduction

• Signal : A physical quantity that varies with time or frequency or any other independent variables

Broad Classification of Signals:

(i) Continuous Time Signal

(ii) Discrete Time Signal

(iii) Digital Signal

Broad Classification of Signals

•Continuous time –•Continuous amplitude

•Continuous time –•Discrete amplitude

•Discrete time –• Continuous amplitude

•Discrete time –•Discrete amplitude

• Analog signals: continuous in time and

amplitude

– Example: voltage, current, temperature,…

• Digital signals: discrete both in time and

amplitude

– Example: attendance of this class, digitizes analog

signals,…

• Discrete-time signals: discrete in time,

continuous in amplitude

– Example: hourly change of temperature

• System : A physical device that operates on an input signal inorder to change/modify the characteristics of that signal into a desired signal.

DT System : y(n) = T{x(n}

Broad Classification of Systems:

(i) Continuous Time System

(ii) Discrete Time System

(iii) Digital System

Why signals should be processed?

• Signals are carriers of information

–Useful and unwanted

–Extracting, enhancing, storing and transmitting the useful information

• How signals are being processed?

– Analog Signal Processing

– Digital Signal Processing

Block Diagram of DSP

PrF ADC DSP DAC PoFAnalog Analog

Equivalent analog signal processor

PrF: antialiasing filtering

PoF: smooth out the staircase waveform

Comparison of DSP over ASP

-Advantages

• Developed Using Software on Computer

• Working Extremely Stable

• Easily Modified in Real Time

• Low Cost and Portable

-Disdvantages

• Lower Speed and Lower Frequency

Basic Ways to Represent DT Signals

�Sequence Representation

�Tabular Representation

�Functional Representation

�Graphical Representation

Discrete Time Signal -Types

(i) Unit sample Sequence

(ii) Unit step sequence

{ }LL ,0,0,1,0,0,0,0

0,1)(

↑=

≠

==

n

nnδ

{ }LL ,1,1,1,0,0,0,0

0,1)(

↑=

<

≥=

n

nnu

Discrete Time Signal – Types (Contd…)

(iii) Ramp Sequence

r(n) = n ; n>0

0 ; n<0

(iv) Exponential Sequence

where x(n) = exp(n)

Rananxn ∈∀= ;,)(

Classification based on Properties

• CT and DT Signals

• Deterministic and Random Signals

• Periodic and Aperiodic Signals

• Symmetric (Even) and Antisymmetric (Odd) Signals

• Energy and Power Signals

• Causal and Non-Causal Signals

Deterministic and Random Signals

• Deterministic Signal – No uncertainity of its magnitude and phase at any given instant of time. (Ex : Sine Signal)

• Random Signal – Charcaterized by uncertainity about its actual occurrence. (Ex: Noise, Speech signal etc)

Periodic and Aperiodic Signals

• Periodic Signal – If the DT signal satisfies the condition

x(n) = x(n+ N)

where N = Fundamental Period

* A signal which repeats itself at regular interval of time is said to be “periodic” otherwise it is “aperiodic”or “non-periodic” signal

Symmetric (Even) and Antisymmetric (Odd) Signals

• Even Signal :

A signal which satisfies the condition x(-n) = x(n)

• Odd Signal :

A signal which satisfies the condition x(-n) = - x(n)

Energy and Power Signals

• A signal is an energy signal if and only if the total energy of the signal is finite and the average power is zero

• A signal is a power signal if the average power of the signal is finite and the total energy is infinite

Causal and Non-Causal Signals

• A DT signal is said to be “causal” if and only if it satisfies the condition

x(n) = 0 for n < 0

In other words, the signal should not exist in the negative part of the time axis.

* The signals which do not satisfy the above condition are “Non- Causal” or “Anti-Causal” Signals.

Discrete Systems

• A Discrete-Time System is a mathematical operation that maps a given input sequence x[n] into an output sequence y[n]

Classification based on Properties

• CT and DT Systems

• Linearity

• Time/Shift Invariance

• Causality

• Stability

• Invertibility

• Static and Dynamic Systems

Linearity

• Linear Systems satisfy “Superposition principle”

Statement :

The response of the system to a weighted sum of signals is equal to the corresponding weighted sum of the outputs of the system to each of the individual input signals.

Time (or) Shift Invariance

• A system is said to be “time/shift invariant” if it satisfies the condition

y(n,k) = y(n-k)

where,

y(n,k) = Delay in the input sequence

by ‘k’ samples

y(n-k) = Delay if the output

sequence by ‘k’ samples

Causality

• Causal System : The response of the system at any instant of time depends only on the present input and/or the past input, but not on the future input.

• Non-Causal/AntiCausal System: Response depends on past output, present and future inputs.

Stability

• BIBO – “Bounded Input Bounded

Output”

* In other words, the sum of the impulse response of the system must yield a finite value for a system to be stable

Invertibility

• A system is said to be invertible if the input signal given to the system can be recovered from the output signal of the system.

Static and Dynamic Systems

• Static System : A system which does not have any memory unit to store the past and/or future input values. In other words, the response of the system depends only on the present input value

• Dynamic System: A system which has a memory unit in it to store the past and/or future input values

�Folding/ Time Reversal

�Time Shifting

�Scaling

- Amplitude Scaling (Constant

Multiplication)

- Time Scaling

(i) Upsampling (ii) Down Sampling

Basic Operations on Sequence

�Signal Addition

�Signal Multiplication

Basic Operations on Sequence (Contd…)

Interconnection of two DT-LTI Systems

• Cascade (series) - Associative Property

• Parallel - Distributive Property

• Combination of Cascade and Parallel

• Feedback

Notes

• Natoms= total charge / electron charge (electrolysis)

• Nmoles = Natoms / Avogadros Number

• Weight (in gram) = Molecular Weight * Nmoles

• Avogadro’s Number = 6.03 * 1023

atoms/mole