Discrete time Signal ,representations and System

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signal and system

Type of representation of discrete time signals

  1. Functional Representation

    { 4 for n=1, 3
    x(n)= { -2 for n =2
    { 0 elsewhere

  2. Tabular method of representation

    n -3 -2 -1 0 1 2 3 4 5
    x(n) 0 0 0 0 4 -2 4 0 0

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  3. Sequence Representation

    X(n) = { 0 , 4 , -2 , 4 , 0 ,……}
    ^ n=0

Table of Contents

Introduction to discrete time signal and system

Signals

A signal is a function of an independent variable (e.g., time) that carries some information or describes some physical phenomenon.

• Notation

-Continuous-time (CT) signal x(t): independent variable t takes continuous values -Discrete-time (DT) signal x[n]: independent variable n takes only integer values

• Examples

– Electrical signals: Voltages and currents in a circuit. – Acoustic signals: Audio and speech signals. – Biological signals: ECG, EEG, medical images.

Applications

The analysis of signals and systems now plays a fundamental role in a wide range of engineering disciplines:

• Speech: recording, compression, synthesis • Music: recording, processing, and synthesis • Petroleum: Seismic surveying and Geological exploration •Telecommunications: AM/FM Radio, speech, mobile phone, and internet

Systems

A system responds to one or several input signals, and its response is described in terms of one or several output signals. This course primarily focuses on single-input single-output (SISO) systems:

• Examples

– An RLC circuit. – The dynamic of an aircraft.

• There are three ways to represent discrete time signals.

1) Functional Representation
{ 4 for n=1, 3
x(n)= { -2 for n =2
{ 0 elsewhere

2) Tabular method of representation
n -3 -2 -1 0 1 2 3 4 5
x(n) 0 0 0 0 4 -2 4 0 0

3) Sequence Representation
X(n) = { 0 , 4 , -2 , 4 , 0 ,……}
^ n=0

STANDARD SIGNAL SEQUENCES

1) Unit sample signal (Unit impulse signal)

δ (n) = 1 n=0
0 otherwise i.e. δ (n)={1}
2) Unit step signal

u (n) = 1 n≥0
0 n<0
3) Unit ramp signal

u (n) = n n≥0
0 n<0
4) Exponential signal
X (n) = a n = (re j Ø ) n = r n e j Ø n = r n (cos Øn + j sin Øn)