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DSP Basics

Chapter 1

ME-4701

Digital Signal Processing

Elective

Spring 2015

SZABIST, Karachi


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Instructor:

Engr. Humera Rafique

Assistant Professor (Mechatronics)

[email protected]

Office: FR-404 (100 Campus )

Course Support

Official: ZABdesk


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Chapter Contents

1. Introduction

2. Signals and Systems

3. Types of Signals

4. Types of Systems


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Introduction to Signal

Processing


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Introduction

System

input output

Excitation Response

signals

Signals and Systems:


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Introduction

Signal:

An entity, a pattern of variations, that carries or translates some information

Input, a stimulus, an excitation to a system or process

Response to a system or process

e.g., electrical pulses, sine wave, audio signal, video signal, TV broadcast etc.

Representation of Signals:

Graphical

Mathematical

Physical


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Introduction

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-1

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Introduction%% DSP lecture Support

% Chapter 1: Introduction to Signal Processing

% Article: Signals and Systems

% grpahical representation

fs = 8000; dt=1/fs; t = 0:dt:1; f= 500;

x = sin(2*pi*f*t); % mathematical representation

plot(t,x), axis([0 0.02 -1 1]),grid, xlabel('Time'), ylabel('Amplitude')

% physical interpretation

wavplay(x,fs)

% saving audio for playback

wavwrite(x,fs,'H:\Fall 13\DSP\MatlabSupp\sinsound')


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Introduction

System:

An electrical/physical unit, comprising of a component, device or a complex

small or large network, capable of processing an input signal to a response

System Components:

1. Excitation (input) x(t)

2. Process (system kernel) h(t)

3. Response (output) y(t)

h(t)

x(t) y(t)


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Introduction

Time domain

Frequency domain

Domain of Signals and Systems:

sin 2

X 24

syms t f;

y = sin(2*pi*f*t);

Y = laplace(y)

pretty(Y)

Graphical

Mathematical

Physical

Signals are represented as a function of one or more variables


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Introduction

Spatial domain

Time-Frequency: Spectrogram

(Hz/Sec)

Domain of Signals and Systems:

Graphical

Mathematical

19 20 21 22 23 24

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8

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Types of Signals


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Signal Types

Signal Classifications:

1. Periodic/Non Periodic signals

2. Continuous time/Discrete time signals

3. Analog/Digital signals

4. Causal/Non-Causal/Anti-Causal signals

5. Even/Odd signals

6. Finite length/Infinite length signals

7. Deterministic/Random signals

8. Real / Complex valued

9. Power and Energy signals


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Signal Types

1. Periodic/Non Periodic signals:

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-0.8

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Time

Ampl

itude

T = 0:1/50E3:10E-3;

D = [0:1/1E3:10E-3;0.8.^(0:10)]';

Y = pulstran(T,D,'gauspuls',10E3,0.5);

plot(T,Y), xlabel('Time'), ylabel('Amplitude')

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fs = 10000; dt = 1/fs; t = 0:dt:1; f = 200;

x = square(2*pi*f*t);

plot(t,x,'.-m','MarkerSize',2), a = size(x); b = zeros(1,a);

axis([0 0.02 -1.1 1.1]), xlabel('Time'), ylabel('Amplitude')

hold, plot(t,b,'-.k'),axis([0 0.02 -1.1 1.1]) % for horizontal axis line


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Signal Types

1. Periodic/Non Periodic signals:

% Dirichlet Function

x = linspace(0,4*pi,300);

plot(x,diric(x,7)); axis tight; title(' Dirichlet Function')

xlabel('Time'), ylabel('Amplitude')

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0

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Dirichlet Function

Time

Ampl

itude

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t

x(t)

Sinc

%% sinc

x = linspace(-5,5); y = sinc(x); % plot(x,y), xlabel('Time'), ylabel('Amplitude')

a = length(x)-1; t = -a/2:a/2;

plot (x,y,'LineWidth',1), xlabel('t'), ylabel('x(t)'), title('Sinc'), hold,

plot(zeros(1,a+1)',t,'-.k') % for vertical axis line

plot(t,zeros(1,a+1)','--k') % for horizontal axis line

axis([-5 5 -0.4 1.1])


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Signal Types

2. Continuous Time/Discrete Time signals:

!"#Discretized time axis

Continuous-time signal x(t), the

independent variable, t is exist at

every instant of time

The signal itself needs not to be

continuous

A Discrete-time signal defined only at

discrete instances

Thus, the independent variable t has

discrete values only

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0 0.002 0.004 0.006 0.008 0.01-1

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DT Am

plitu

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Signal Types

2. Continuous Time/Discrete Time signals:

%% continuous and discrete signals

fs = 8000; dt = 1/fs; t = 0:dt:1; f = 500;

x = sin(2*pi*f*t);

subplot(211), plot(t,x)

axis([0 0.01 -1 1]),grid

xlabel('Time')

ylabel('Amplitude')

subplot(212)

stem(t,x,'g','filled')

axis([0 0.01 -1 1]),grid

xlabel('Time')

ylabel('DT Amplitude')

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Signal Types

3. Analog /Digital signals:

Discretized amplitude axis

undiscretized time axis: : Piecewise

continuous time signal

Discretized amplitude axis

Discretized time axis


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Signal Types4. Causal /Anti causal/Non-Causal signals:

Causal:

0 % 0


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Anti-Causal: 0 & 0


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Non-Causal:

0'()**+ & 0, % 0


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Signal Types

5. Even/Odd signals:

-An even signal is symmetric around the vertical axis

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t

x(t)

Even Signal

x = [ zeros(1,10) ones(1,5) zeros(1,10)];

a = length(x)-1; t = -a/2:a/2;

plot (t,x,'c','LineWidth',2), axis([-12 12 -0.1 1.1]), xlabel('t'), ylabel('x(t)'), title('Even Signal')

hold, plot(zeros(1,a+1)',t,'-.k') % for vertical axis line

plot(t,zeros(1,a+1)','--k') % for horizontal axis line


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Signal Types

5. Even/Odd signals:

--An odd signal is symmetric around the horizontal axis

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000-4

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0

1

2

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t

x(t)

Odd Signal

-

--%% oddfs = 8000; dt = 1/fs; t = 0:dt:1; f = 500;

x = sin(2*pi*f*t);

a = length(x)-1; t = -a/2:a/2; plot(t,angle(fft(x))), grid

xlabel('t'), ylabel('x(t)'), title('Odd Signal')


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Signal Types6. Finite Length / Infinite Length signals:

Finite length:

0 50 100 150 200 250 300-1

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Signal Types6. Finite Length / Infinite Length signals:

Infinite length:

0 0.005 0.01 0.015 0.02 0.025 0.03-1

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0

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. . . . . . .. . . . . . .


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Signal Types

7. Real/Complex Valued signals:

| | Real valued:

12 Complex valued:

| | 2

34 56 2


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Signal Types

8. Deterministic / Random signals:

3 *589 Deterministic signal that can be represented by an equation, formula or table Future values are predictable

Linear signals

Random signals whose representation is not possible

to by a usual mathematical equation, formula or table

Thus, future values are not predictable (a statistical

procedure can work)

Non-linear, stochastic or un-deterministic signals

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Signal Types

8. Deterministic / Random signals:

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-1

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Random Signal

Time

Ampl

itude

%% random signal

x = randn(1,50);

plot(x), grid, axis tight;

title('Random Signal'),

xlabel('Time'), ylabel('Amplitude')

5 10 15 20 25 30 35 40 45 50-2

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Random Signal

Time

Ampl

itude

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-2

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2Random Signal

Time

Ampl

itude


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Signal Types

9. Power / Energy signals:

: lim=>1

2@ 1 A =

BC5=

Energy of a Signal:

D A >

BC5>

Power of a Signal:

* E | |,F

5F

) limF>12E | |,

F

5F


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Signal Types


Energy Signal:

Power Signal:

)G* 0; **I+ *

)G* *; **I+ 0

All the periodic signals are power signals, but

Not all non-periodic signals are energy signals


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Signal Types


Example 1-1:

Find out if the signal is energy, power or neither?

x(t)

t

3

1

0

x(n)

n

0

1 2


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Signal Types


Example 1-2: Find out if the signal is energy, power or neither?

3 sin 2 - J J


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Types of Systems


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System Types

System Classifications:

1. Continuous time/Discrete time systems

2. Analog/Digital systems

3. Linear/Non-linear systems

4. Time variant/ Time-invariant systems

5. Causal/Non-causal systems

6. Open loop/Closed loop systems

7. Stable/Unstable systems

8. Static /Dynamic Systems


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System Types

Continuous /Discrete Systems:

Continuous Time

System

Discrete Time

System


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System Types

Analog/Digital Systems:

Analog System

Digital System111011110001. . . . . . . . 101010010001. . . . . . . .


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System Types

Linear/Non-Linear Systems:

Linear System6 +

Linear System

6 +

+6 +

Linear System +


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System Types

Time Variant/Time Invariant Systems:

Time inVariant

6 +

6 - L + - L

Time Variant

6 +

6 - L + - L


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System Types

Causal / Non-causal Systems:

Causal: A system whose, output depends on current and past inputs, no contribution from the future

inputs

Real time systems

+ - 2

+ 2

Non-Causal: A system whose, output depends on future and past inputs


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System Types

Open Loop / Closed Loop Systems:

+ - 2

+ 2 - + - 1

Open Loop System6 +

Closed Loop System6 +


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System Types

Stable / Unstable Systems:

Stable System6 stableinput + 2*S)S

Unstable System6 stableinput +6 S2*S)S


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System Types

Static / Dynamic Systems:

Static Systems: Constant system, whose parameters do not change

Memoryless systems (i.e., No feedback element)

e.g., constant target shooting system

Dynamic Systems: whose parameters change

Memory based systems

e.g., human body, missile system that tracks moving target

+ 6 - 2

+ 6+ 2+ 6+ - 217-Jan-15 HR Spring 2015 43

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Reference

1. Proakis

2. Orfanidis

3. Mathworks Manual: Signal processing toolbox


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Documents

DSP1 Basics