DIGITAL SIGNAL PROCESSING

LAB Tutorial-01

Prepared by: Mekonen A.

DDIT, SECE 2019 G.C
 Out lines
ou

 Basics of MATLAB and its Operations

 Basics of Discrete Time Signals
 Operations on Discrete Time Signals
 Discrete Time Systems (Linear Convolution)
 What is MatLab?

MatLab stands for = Matrix Laboratory

Is an interactive, matrix-based system for scientific and engineering
numeric computation and visualization

It integrates numerical analysis, matrix computation, signal processing and
graphics in an easy-to-use

MatLab has a number of add-on software modules, called toolboxes, that
perform more specialized computations.

Used for Signal processing and analysis

Modelling of dynamical systems

Solving partial differential equations

Simulation of engineering systems

Matrix computations and linear algebra

MatLab is case sensitive (‘A’ is a different variable from ‘a’)
 MatLab Desktop Interfaces/windows
 Command window : is where we type the commands
and instructions that cause MatLab to evaluate, compute,
draw and perform all the other wonderful results
Command History: contains a running history of the
commands that you type into the Command Window
Current Folder : displays contents of current working
directory or access your files
Work space : shows the variables you have created
Editor Window :use to edit individual entries
in a vector or matrix
 Some Useful MatLab Commands

what: List all m-files in current directory

dir: List all files in current directory

ls: Same as dir.

pwd: Show current directory
whos: gives a complete listing of all variables currently defined and the size of those variables

Who: simply lists all variable names currently in use

clear all: clear all variables from workspace window

clear a,b: will simply clear variables a and b
close all: used to close all figure windows

clc: used to clear command windows

edit: used to open editor window

exit/quit: used to close matlab
 Simple MatLab Commands for Plotting
Plot: plotting in a linear coordinate as continuous function.

Stem: plot in a linear coordinate as discrete time.

hold on :Allows multiple plots to be superimposed on the same
axes.

Figure: Create a figure for plotting

hold off: Release hold on current plot

subplot(a,b,c): Create an a × b matrix of plots with c the current
figure

grid: Adds a grid to the plot
xlabel: Labels x-axis ylabel: Labels y-axis
 Some Built-in Math Functions

MATLAB comes with a large number of built-in functions that operate on

matrices on an element-by element basis

sin: sine

cos: cosine

tan: tangent

asin: inverse sine

acos: inverse cosine

atan: inverse tangent

exp: exponential (e=2.7183)

log: natural logarithm

log10: common logarithm

sqrt: square root

abs: absolute value
 Matrix Operations

MatLab contains a number of arithmetic, relational, and logical operations on

matrices
+ addition
- subtraction
* multiplication
/ right division
\ left division
^ exponentiation (power)
’ conjugate (transpose)
< less than
<= less than or equal to
> greater than
>= greater than or equal to
== equal to
~= not equal to
 Graphing a Signal Using MatLab
Consider a discrete sine wave signal defined as follows
Cont’d
y(k) = 5sin(0.2k), k = 0, 1, 2, …. , 50
This signal takes on values every 0.2 seconds starting at 0 seconds
and ending at 10 seconds
%MatLab program for graphing the signal
• k=0:1:50; %k=[0, 1, 2, . . . 50]
• t=0.2*k; %t=[0, 0.2, 0.4, . . . 10]
• y=5*sin(0.2*k); subplot(1,2,1)
• plot(t,y,'b’); title('y=5*sin(0.2*k)’); xlabel('time in (sec)');
• ylabel('Amplitude’); grid on; subplot(1,2,2)
• stem(t,y,'r’); title('y=5*sin(0.2*k)in discrete form');
• xlabel('n sample number’); ylabel('Amplitude'); grid on
 Cont’d
Product of Sinusoidal Signals
•% MatLab Program for Multiplication of Two signals
•t=0:0.01:2;
•y=sin(2*pi*t).*sin(2*pi*4*t);
•subplot(2,1,1)
•plot(t,y);title('multiplication of two signals' );
•xlabel('time in (sec)' ); ylabel('Aplitude'); grid on
•subplot(2,1,2)
•stem(t,y,'k’);
•title('multiplication of two signals' );
•xlabel('number of sapling’ ); ylabel('Aplitude’);
•grid on
 Basic Discrete Time Signals
Unit Impulse Signal (Unit Sampling Sequence)
Unit Step Signal (Unit Step Sequence)
Generation of exponential sequence
Real-valued Exponential Sequence
Complex-valued Exponential Sequence
 Unit Impulse Signal(Unit Sample Sequence)
 (n)=1, for only n=0, and else in everywhere it has the
amplitude value zero (for n  0).
 (n-n0)=1, for n=n0, and else in everywhere it has the
amplitude zero for (n  n0).
program on MatLab
function[x,n]=impseq(n0,n1,n2)
%Generates x(n)=delta(n-n0);n1<=n<=n2;
%[x,n]=impseq(n0,n1,n2)
n=(n1:n2);
x=((n-n0)==0);
 Unit step signal

u(n) = 1 for n ≥ 0 ,
= 0 for n < 0

U(n-n0)= 1 for n ≥ n0, for a shifted signal by an n0
0 for n < n0
program on matlab
function[x,n]=stepseq(n0,n1,n2)
%Generates x(n)=u(n-n0);n1<=n<=n2
%[x,n]=stepseq(n0,n1,n2);
n=(n1:n2);
x=((n-n0)>=0);
 Generation of Exponential Sequences
%Generation of exponential sequences
n=input('Enter the length of
exponential sequence');
t=0:n;
a=input('Enter the value of a');
y=exp(a.*t);
stem(t,y,'r');
xlabel(‘Index number');
ylabel('Amplitude');
title('Generation of exponential
sequence');
 Real-valued Exponential Sequence
 x(n) = ∀n; a ∈ R
 example: generate x(n) = , for 0 ≤ n ≤ 10
generate x(n) = , for 0 ≤ n ≤ 10
programing on matlab >> y=exp((1.11).^n);
>> n=[0:10];
>> subplot(2,2,2)
>> x=exp((0.9).^n);
xlabel('n sequences')
>> subplot(2,2,1)
>> xlabel('n sequences')
ylabel(‘y=exp((1.11).^n
>> ylabel(‘x=exp((0.9).^n’)) ’))
>> title('real-valued sequence') title('real valued sequence')
>> stem(n,x) stem(n,y,'r')
 Complex-valued Exponential Sequence
n=[0:10];
x=exp((2+3i)*n); subplot(1,2,1);
stem(n,real(x)); xlabel(‘(a) n sequences');
ylabel('Amplitude of x');
title('plotting the real part')
Subplot(1,2,2);stem(n,imag(x));
xlabel(‘(b) n sequences');
ylabel(‘Amplitude of imaginary sequence')
title('plotting the imaginary part')
subplot(1,2,3); stem(n,angle(x)*(180/pi));
xlabel(‘(c) n sequences');
ylabel('angle in degrees')
title('plotting the angles in(degrees)')
 Basic Discrete Time Signal Operations
 Signal Addition
Signal Multiplication
Signal Scaling (Constant Multiplier)
Time Shifting
Signal Folding (Time Reversal)
 Signal Addition
>> n1=0:6;
>> n2=2:8;
>> x1=rand(size(n1));
>> x2=rand(size(n2));subplot(2,2,1);
>> stem(n1,x1,’k’);title(‘The first
sequence’);
>> Subplot(2,2,2);
>> stem(n2,x2,'r');title(‘The second
sequence’);
>> [y,n]=sigadd(x1,n1,x2,n2);
>> stem(n,y,’b’)
>> title('signal addition');
>> xlabel('number of sequences');
>> ylabel('Amplitude of signals');
 Cont’d
x=input('ENTER THE FIRST SEQUENCE:');
subplot(3,1,1);
stem(x);
title('X=The 1st signal');
y=input('ENTER THE SECOND SEQUENCE:');
subplot(3,1,2);
stem(y);
title('Y=The 2nd signal');
z=x+y;
disp(z)
subplot(3,1,3);
stem(z);
title('The addedd signal is(Z=X+Y)');
 Signal Multiplication
n1=1:6;
>> n2=0:5;
>> x1=[1 2 1 2 2 1];
>> x2=[2 4 5 6 4 2];
>> subplot(2,2,1); stem(n1,x1,'b');
>> title('plotting the first sequence');
>> subplot(2,2,2); stem(n2,x2,'k');
>> title('plotting the second sequence');
>> subplot(2,2,3)
>> [y,n]=sigmult(x1,n1,x2,n2); stem(n,y,'r');
>> title('signal multiplication');
>> xlabel('n sequences of two signals');
>> ylabel('The result of multiplied signal')
 Signal Scaling
>> x=[2 3 4 5 6];
>> n=0:4;
>> subplot(2,2,1)
>> stem(n,x); xlabel('n index')
>> ylabel('Amplitude of the signal')
>> title('The first signal');
>> y=-1*x; subplot(2,2,2); stem(n,y,'r’)
>> xlabel('n index');
>> ylabel('The Amplitude of the scaled
signal');
>>title('scaling with a constant number')
>> grid on
 Time Shifting
function [y,n] = sigshift(x,m,k)
% implements y(n) = x(n-k)
% [y,n] = sigshift(x,m,k)
n = m+k; y = x;
On command window write the following
>> m=0:4;
>> x=[1 2 4 6 2 4];
>> [y,n]=sigshift(x,m,2);
>> stem(m,x,'r')
>> [y1,m]=sigshift(x,m,2);
>> hold on
>> stem(m,y1,’b’)
 Folding Signal (Time Reversal)
Programming on MatLab
>> x=[2 6 4 2];
n=[0:3];
stem(n,x,'k')
hold on
[y,n]=sigfold(x,n);
stem(n,y,'r');
>>legend('1st signal','folded signal');
>> title(Time Reversed signal');
>> xlabel('n index number');
>> ylabel(‘magnitude the of the signal')
 Cont’d
• x=input('ENTER THE SEQUENCE x(n)=');
• N=input('Enter length of the sequence
N=');
• n=0:N-1;
• subplot(2,1,1); stem(n,x,'k'); grid on
• title('Signal x(n)');
• y=fliplr(x);
• m=fliplr(-n);
• disp('FOLDED SEQUENCE')
• disp(y)
• subplot(2,1,2);
• stem(m,y,'r'); grid on
• title('Reversed Signal x(-n)') ;
 Linear Convolution (Convolution Sum)
x=input('ENTER THE INPUT SEQUENCE of x(n)=');
nx=length(x);n1=0:1:nx-1;
h=input('ENTER THE IMPULSE RESPONSE of
h(n)=');
nh=length(h);n2=0:1:nh-1;
y=conv2(x,h); n3=0:1:nx+nh-2; subplot(2,2,1);
stem(n1,x,'b'); xlabel('(a) n-index');
ylabel('Amplitude of x(n)');subplot(2,2,2);
stem(n2,h,'k'); xlabel('(b) n-index');
ylabel('Amplitude of h(n)');subplot(2,2,3);
stem(n3,y,'r'); xlabel('n sampling
sequences');
ylabel('Amplitude of y(n)');
title('convolution of x(n) with h(n)');
disp('The resultant signal is');y;
 Cont’d
x=[1 2 3 4 3 2 1];
nx=length(x); n=0:1:nx-1;
subplot(2,2,1); xlabel('(a)n– index’);
ylabel(x(n)');
title('input sequence of x(n)');
stem(n,x'k');
h=[4 2 3 1 3 2]; nh=length(h); m=0:1:nh-1;
subplot(2,2,2); xlabel('(b)n index’);
ylabel('h(n)');
title('impulse response of h(n)');
stem(m,h,'b');
y=conv2(x,h); ny=0:1:nx+nh-2;
subplot(2,1,2); xlabel('(c)n--index');
ylabel('y(n)’);
title('convolution of two sequences x(n)and h(n)');
stem(ny,y,'r');
disp('The resultant signal is ');y;
 Cont’d
• x=[4 3 5 5];
• nx=length(x); n=0:1:nx-1;
• subplot(2,2,1); stem(n,x,'k');grid on
• xlabel('(a)n– index'); ylabel('x(n)’);
• title('input sequence of x(n)');
• h=[-1 1 2]; nh=length(h); m=0:1:nh-1;
• subplot(2,2,2); stem(m,h,'b');grid on
• xlabel('(b)n-- index');ylabel('h(n)')
• title('impulse response of h(n)');
• y=conv2(x,h);ny=0:1:nx+nh-2;
• subplot(2,1,2); stem(ny,y,'r');grid on
• xlabel('(c)n--index');
• ylabel('y(n)’);
• title('convolution of two sequences x(n)and h(n)');
• disp('The resultant signal is ');y;
THANK YOU!