Lab Manual of Analog & Digital Communication
Experiment # 3
Communication Signals: Operations
Objective
• To learn the use of MATLAB for different operations on signals.
• To develop a thorough understanding of communication signals and their basic
operations as used in Communication.
SUMMARY
• Signal operations (Scaling, Shifting, Folding, Sample Summation, Sample product,
Energy, Even and Odd sequences, Convolution)
SIGNAL OPERATIONS:
1. Scaling:
In this operation the samples of the signal is multiplied by a scalar α. The
mathematical operator * is used for the implementation of the scaling property.
α{x(n)} = { α x(n)}
>> [x,n] = stepseq (-1,-5,5);
>> a = 2;
>> y = a*x;
>> subplot (2,1,1);
>>stem (n,x);grid on;
>> subplot (2,1,2);
>> stem (n,y, 'r');
>> grid on;
2. Shifting
In this operation, each sample of the signal is shifted by k to get a shifted
signal. By definition: y(n) = {x (n-k)}
In this operation there is no change in the array or vector x, that contains the samples of
the signal. Only n is changed be adding k to each element. The function is given below:
function [y,n] = sigshift (x,m,n0)
% implement y(n) = x(n-n0)
Lab Manual of Analog & Digital Communication
% x = samples of original signal
% m = index values of the signal
% n0 = shift amount , may be positive or negative
% [y,n] = sigshift(x,m,n0)
n = m+n0;
y = x;
See the example of above function:
%Example 3.1
% This example demonstrate the use of stepseq, sigshift, sidadd & sigmult
function clc; clear;
[x,n] = stepseq (0,-
10,10); subplot (3,2,1);
stem (n,x);
axis ([-12 12 0
3]); grid on;
xlabel ('n');
ylabel
('x(n)');
title ('Original Signals');
[y1,n1] = sigshift(x,n,2.5);
subplot (3,2,2);
stem (n1,y1); axis ([-12 12 0 3]); grid on;
xlabel ('n');
ylabel
('y1(n)');
title ('Shifted signal,x(n-2.5)');
Lab Manual of Analog & Digital Communication
%
[y2,n2] = sigshift (x,n,-2.5);
subplot (3,2,4);
stem (n2,y2);
axis ([-12 12 0 3]);
grid on;
xlabel ('n');
ylabel ('y2(n)');
title ('Shifted signal,x(n+2.5)');
[y_add,n_add] = sigadd(y1,n1,y2,n2);
subplot (3,2,6);
stem (n_add,y_add,'r');
axis ([-12 12 0 3]);
grid on;
xlabel ('n');
ylabel ('y1(n) + y2(n)');
title ('Added Signal');
[y_mul,n_mul] = sigmult(y1,n1,y2,n2);
subplot (3,2,5);
stem (n_mul,y_mul,'k');
axis ([-12 12 0 3]);
grid on;
xlabel ('n');
ylabel ('y1(n) * y2(n)');
title ('Multiplied Signal');
%
Lab Manual of Analog & Digital Communication
Figure 3.1
3. Folding:
In this operation each sample of x(n) is flipped around n=0 to obtain a folded
signal y(n). y (n) = {x(-n)}
In MATLAB, this function is implemented by using a built-in function fliplr(x) and –
fliplr(x). Its implementation is given below:
function [y,n] = sigfold(x,n)
% implements y(n) = x(-n)
% [y,n] = sigfold(x,n)
% x = samples of the original signal
% n = indexes of the original signal
y = fliplr(x);
n = -fliplr (n);
Do its example by yourself from any example signals.
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Lab Manual of Analog & Digital Communication
4. Sample Summation:
This operation is different from sigadd function. In this operation we add all the sample
values of any signal x(n) between any two of its index values. By definition
∑ x(n) = x(n1) +………+x(n2)
In MATLAB it is implemented by the sum(x(n1:n2)) command. See the code below for the
demonstration of above function.
>> [x,n] = stepseq (5,0,10)
>> sum(x(2:7))
5. Sample Product:
This operation also differs from the sigmult function. It implies the sample values over the
range n1:n2. It is implemented by the prod(x(n1:n2)). See the code below.
>> x = [0 1 2 3 4 5]
>> prod(x(2:5))
6. Energy:
The energy of any signal x is computed by the mathematical relation:
Ex = ∑ x(n) x*(n) = ∑│x(n)│2
Where the subscript * is used for complex conjugate of the signal x. The energy of the finite
duration signal is computed in MATLAB as.
>> Ex = sum (x.*conj(x));
Or
>> Ex = sum (abs(x).^2);
7. Even and Odd Sequence:
A real valued sequence xe(n) is called even if the following condition satisfies.
xe(-n) = xe(n)
Similarly a signal is said to be an odd signal if
xo(-n) = -xo(n)
See the example below:
%example 3.2
% Generation of even and odd signals
n1 = [0:0.01:1];
Lab Manual of Analog & Digital Communication
x1 = 2*n1;
n2 = [1:0.01:2];
x2 = -2*n2+4;
n = [n1,n2];
x = [x1,x2];
%Even Signal
[xe,ne] = sigfold(x,n);
%Plotting of original signal
subplot (3,1,1);
plot (n,x);
axis ([-4 4 0 2.5]);
grid on;
%Plotting of original signal + even signal
subplot (3,1,2);
plot (n,x/2,ne,xe/2);
axis ([-4 4 0 2.5]);
grid on;
% Plotting of original signal + odd
signal xo = -xe;
no = ne;
subplot (3,1,3);
plot (n,x/2,no,xo/2);
axis ([-4 4 -2.5 2.5]);
grid on;
Lab Manual of Analog & Digital Communication
Figure 3.2
The above example shows to develop the even and odd signals from a given signal. Now we
are going to develop a function to compute the even and odd signals for ourselves. See the
code of function file below:
function [xe,xo,m] = evenodd (x,n)
% Decomposes a real function into its even and odd parts
% [xe,xo,m] = evenodd(x,n)
% xe = even signal
% xo = odd signal
% m = indexes
% x = original signal
% n = indexes for original signal
if any(imag(x)~=0)
error(‘x is not a real sequence’)
end
m = -fliplr(n);
m1 = min([m,n]);
m2 = max([m,n]);
m = m1:m2;
nm = n(1)-m(1);
Lab Manual of Analog & Digital Communication
n1 = 1:length(n);
x1 = zeros(1,length(m));
x1(n1+nm) = x;
x = x1;
xe = 0.5*(x+fliplr(x));
xo = 0.5*(x-fliplr(x));
Now change the example 3.2 code to implement the same example with this
function.
8. Convolution:
The convolution is very important operation as far the system as their impulse responses are
concern. It is mathematically defines as:
y (n) = x(n) * h(n)
Where h(n) is the impulse response of the system. The above definition is best depicted by
the following diagram.
In MATLAB convolution is implemented by the following instructions.
>> x = [1 5 3 9 1 2 3 8 5 -3 0 4];
>> h = [1 0 2 3];
>> y = conv(x,h);
A function is developed which will evaluate convolution in a more precise form and also
calculate the indexes to help us plot the sequences.
function [y,ny] = conv_m(x,nx,h,nh)
% Modified convolution routine for signal processing
% [y,ny] = conv_m(x,nx,h,nh)
% [y,ny] = convolution result
% x = original signal
% nx = index values
% h = impulse response signal
% nh = index values for impulse response
nyb = nx(1) + nh(1);
Lab Manual of Analog & Digital Communication
nye = nx(length(x)) + nh(length(h));
ny = [nyb:nye];
y = conv(x,h);
POST LAB
a. x(n) = u(n) – u(n-5). Decompose into even and odd components and plot them.
b. n = [-2:2]
x1 = [3,2,1,-2,-3];
x2 = [1,1,1,1,1]
Implement y = x1*x2
