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ITM UNIVERSE Signal & System
140953109008 Page1 EE A
Lab 1: Introduction to MATLAB
AIM: Introduction to MATLAB
INTRODUCTION:
MATLAB stands for Matrix Laboratory. MATLAB is a high-performance language for
technical computing. It integrates computation, visualization, and programming in an easy-to-
use environment where problems and solutions are expressed in familiar mathematical
notation. Typical uses include
 Math and computation
 Algorithm development
 Data acquisition
 Modelling, simulation, and prototyping
 Data analysis, exploration, and visualization
 Scientific and engineering graphics
 Application development, including graphical user interface building.
The MATLAB System:
The MATLAB system consists of five main parts:
 Development Environment. This is the set of tools and facilities that help you use
MATLAB functions and files. Many of these tools are graphical user interfaces. It
includes the MATLAB desktop and Command Window, a command history, an
editor and debugger, and browsers for viewing help, the workspace, files, and the
search path.
 The MATLAB Mathematical Function Library. This is a vast collection of
computational algorithms ranging from elementary functions, like sum, sine, cosine,
and complex arithmetic, to more sophisticated functions like matrix inverse, matrix
eigen values, Bessel functions, and fast Fourier transforms.
 The MATLAB Language. This is a high-level matrix/array language with control
flow statements, functions, data structures, input/output, and object-oriented
programming features. It allows both "programming in the small" to rapidly create
quick and dirty throw-away programs, and "programming in the large" to create large
and complex application programs.
 Graphics. MATLAB has extensive facilities for displaying vectors and matrices as
graphs, as well as annotating and printing these graphs. It includes high-level
functions for two-dimensional and three-dimensional data visualization, image
processing, animation, and presentation graphics. It also includes low-level functions
that allow you to fully customize the appearance of graphics as well as to build
complete graphical user interfaces on your MATLAB applications.
 The MATLAB Application Program Interface (API). This is a library that allows
you to write C and Fortran programs that interact with MATLAB. It includes facilities

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for calling routines from MATLAB (dynamic linking), calling MATLAB as a
computational engine, and for reading and writing MAT-files.
MATLAB Desktop:
When we start MATLAB, the MATLAB desktop appears, containing tools (graphical user
interfaces) for managing files, variables, and applications associated with MATLAB. The
following illustration shows the default desktop. You can customize the arrangement of tools
and documents to suit your needs.
MATLAB Windows:
1. MATLAB Desktop:
It consists of following sub windows.
a) Command Windows: This is the main window. It is characterized by the MATLAB
command prompt (>>).
b) Current Directory: This is where all your files from the current directory are listed. You
can do file navigation here.
c) Workspace: It lists all variables that you have generated so far and shows their types and
sizes.

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d) Command History: All commands typed on the MATLAB prompt in the command
window get recorded, even across multiple sessions.
2. Figure Window:
The output of all graphics command typed in the command window is flushed to the figure
window.
3. Editor Window:
This is where you can write edit, create and save your own programs in files called m files.
MATLAB on the Windows System:On the windows systems, MATLAB is started by
double clicking the MATLAB icon on the desktop or by selecting MATLAB from the start
menu.
The starting procedure takes the user to the command window where the command line is
indicated with '>>'.
Help and information on MATLAB commands can be found in several ways.
 From the command line by using the ‘help <topic name>' command.
 From the separate Help window found under the Help menu.
Prototype M-Files:
When you use the mfile name option with load library, MATLAB generates an M-file called
a prototype file. This file can then be used on subsequent calls to load library in place of a
header file.
Scripts:
When you invoke a script, MATLAB simply executes the commands found in the file.
Scripts can operate on existing data in the workspace, or they can create new data on which to
operate. Although scripts do not return output arguments, any variables that they create
remain in the workspace, to be used in subsequent computations. In addition, scripts can
produce graphical output using functions like plot.
Functions:
Return information about a function handle
SyntaxS = functions(funhandle)
Description:
S = functions(funhandle) returns, in MATLAB structure S, the function name, type, filename,
and other information for the function handle stored in the variable funhandle.

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Aim 1: Define two random matrix A&B . find A+B,A-B,A*B,eigenvalues
of A, inverse of A, rank of A.
Software Required:
MATLAB 2013
Input:
A = [1 2;6 7]
A_eig=eig(A)
B = [2 7;9 1]
B_eig=eig(B)
A_inv=inv(A)
B_inv=inv(B)
A_rank=rank(A)
B_rank=rank(B)
Output:
A =
1 2
6 7
A_eig =
-0.5826
8.5826
B =
2 7
9 1
B_eig =
9.4530
-6.4530
A_inv =
-1.4000 0.4000
1.2000 -0.2000
B_inv =
-0.0164 0.1148
0.1475 -0.0328
A_rank = 2
B_rank = 2

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Aim 2: y=(x*2)+4*x+3 defined x from 0 to 200 in steps of 20.plotits discrete
samples.
Software Required:
MATLAB 2013
Input :
x=0:20:200
y=x.^2+4*x+3
stem(x,y);xlabel('x');ylabel('x^2+4*x+3');title('function');
output :
Aim3 : 0 to 360 steps of 10 y=(cos(x)).^2+4*sin(x).
Software Required:
MATLAB 2013
Input :
x=0:10:360
y=(cos(x)).^2+4*sin(x)
subplot(3,1,1),plot(x,cosd(x));xlabel('degrees');ylabel('amplitude');title('coswave');grid on;
subplot(3,1,2),plot(x,sind(x));xlabel('degrees');ylabel('amplitude');title('sinewave');grid on;
subplot(3,1,3),plot(x,y); xlabel('degrees');ylabel('amplitude');title(' y=(cos(x)).^2+4*sin(x)
0 20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
4
x
x2+4*x+3
function

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');grid on;
Output:
Aim 5: Define x in degrees and plot cos (x), sin (x) and tan (x)
Software Required:
MATLAB 2013
Input:
(a) sin (x)
x = 0 : 0.1 : 2*pi;
y1 = sin(x);
plot(x, y1); ylabel('amplitude');title('sin wave');

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(b) cos (x)
x = 0 : 0.1 : 2*pi;
y2 = cos(x);
plot(x, y2) ; ylabel('amplitude');title('cos wave');
(c) tan (x)
x = 0 : 0.1 : 2*pi;
y3 = tan(x);
plot(x, y1) ; ylabel('amplitude');title('tan wave');
Output:
(a)
(b)

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(c)

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Conclusion:
After performing this experiment we studied about MATLAB and its basic operations and
functions.

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LAB. : 2 Signal Generation
Aim 1:Plot (a)sine wave and (b)cosine wave in continues time signal.
Software Required:
MATLAB 2013
Input:
(a) sin wave
f=50
Fs=1000;
Ts=1/Fs
nts=0:Ts:1/f
s=sin(2*pi*f*nts);
plot(nts,s);xlabel('time');ylabel('amplitude');title(‘sine wave’);grid on;
(b) cosine wave
f=50
Fs=1000
Ts=1/Fs
nts=0:Ts:1/f
s=cos(2*pi*f*nts);
plot(nts,s);xlabel('time');ylabel('amplitude');title('cos wave');grid on;

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output: (a)
(b)

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Aim 2:Plot (a)sine wave and (b)cosine wave in discrete time signal.
Software Required:
MATLAB 2013
Input:
(a)
f=50
Fs=input('sampling frequency');
Ts=1/Fs
n=0:Ts:Fs/f
s=sin(2*pi*f*n*Ts);
stem(n,s);xlabel('fre.');ylabel('amplitude');title('sin wave)');
(b)
f=50
Fs=1000
Ts=1/Fs
nts=0:Ts:1/f
s=cos(2*pi*f*nts);
stem(nts,s);xlabel('fre.');ylabel('amplitude');title('cos wave');

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Output: (a) &(b) respectively
0 2 4 6 8 10 12 14 16 18 20
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
fre.
amp. sine wave
0 2 4 6 8 10 12 14 16 18 20
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
fre.
amp.
cosine wave

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Aim3:Plot unit ramp function (Both in CT & DT domain).
Software Required:
MATLAB 2013
Input:
(a)
Fs=200
Ts=1/Fs
n=-50:1:50
[a,b]=size(n)
for i=1:b
if n(i)>=0
ramp(i)=n(i)
else ramp(i)=0
end
end
plot(n,ramp);xlabel('n');ylabel('ramp');title ('Unit_Ramp');grid on
(b)
Fs=200
Ts=1/Fs
n=-50:1:50
[a,b]=size(n)
for i=1:b
if n(i)>=0
ramp(i)=n(i)
else ramp(i)=0
end
end
stem(n,ramp);xlabel('n');ylabel('ramp');title ('Unit_Ramp');grid on
output:
(a)

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(b)

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Aim4: plot unit step function.(Both in CT & DT domain)
Software Required:
MATLAB 2013
Input:
(a)
Fs=200
Ts=1/Fs
nTs=-2:Ts:2
[a,b]=size(nTs)
for i=1:b
if nTs(i)>0
step(i)=1
else step(i)=0
end
end
plot(nTs,step);xlabel('nTs');ylabel('step');title ('unit step');grid on
(b)
Fs=200
Ts=1/Fs
nTs=-2:Ts:2
[a,b]=size(nTs)
for i=1:b
if nTs(i)>0
step(i)=1
else step(i)=0
end
end
stem(nTs,step);xlabel('nTs');ylabel('step');title ('unit_step');grid on
output:
(a)

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(b)

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Aim5 :plot delta function in (a) continuos and (b) descrete time signal.
Software Required:
MATLAB 2013
Input:
(a)
Fs=200
Ts=1/200
nTs=-0.2:Ts:0.2
[a,b]=size(nTs)
for i=1:b
if nTs(i)==0
delta(i)=1
else
delta(i)=0
end;
end;
plot(nTs,delta);xlabel('nTs');ylabel('amplitude');title('delta continous');grid on;
(b)
Fs=200
Ts=1/200
nTs=-0.2:Ts:0.2
[a,b]=size(nTs)
for i=1:b
if nTs(i)==0
delta(i)=1
else
delta(i)=0
end;
end;
stem(nTs,delta);xlabel('nTs');ylabel('amplitude');title('Delta Discrete time');grid on;
output
(a)

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(b)
Aim 6: plot sinc function in (a)continous(b)descrete time signal.

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Software Required:
MATLAB 2013
Input:
(a)
f=50
Fs=2000
Ts=1/Fs
nTs=-.5:Ts:.5
s=sin(2*pi*f*nTs);
sinc_s=s./(2*pi*f*nTs);
plot(nTs,sinc_s);xlabel('time');ylabel('amplitude');title('sinc continuous signal');grid on;
(b)
f=50
Fs=2000
Ts=1/Fs
nTs=-.5:Ts:.5
s=sin(2*pi*f*nTs);
sinc_s=s./(2*pi*f*nTs);
stem(nTs,sinc_s);xlabel('time');ylabel('amplitude');title('sinc descrete signal');
Output:(a)
(b)

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CONCLUSION:
After performing this experiment we studied about different function and their waveform in
both continuous time and discrete time domain.

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LAB. : 3 Sampling Theorem
Aim 1 : Show effectof sampling effect of sampling frequency & prove
nyquist criteria for sampling.
Software Required:
MATLAB 2013
Input:
f=3
Fs1=1.5*f%Fs1<2*f
nTs1=0:1/Fs1:2/f
s=sin(2*pi*f*nTs1)
figure;
plot(nTs1,s);hold on; stem(nTs1,s);hold off;xlabel('nTs');ylabel('Amplitude');title('Discrete
sine wave Fs<2Fm');
f=3
Fs2=2*f%Fs2=2*f
nTs2=0:1/Fs2:2/f
s=sin(2*pi*f*nTs2)
figure;
sine wave Fs=2Fm');
f=3
Fs3=5*f%Fs3>2*f
nTs3=0:1/Fs3:2/f
s=sin(2*pi*f*nTs3)
figure;
sine wave Fs>2Fm');

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output:

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Aim 2 : Add different harmonics of sin wave having tone frequency 50 hz.
Software Required:
MATLAB 2013
Input :
f=2;
fs1=25*f;
t1=0:1/fs1:1;
s1=sin(2*pi*f*t1)+sin(2*pi*2*f*t1)+sin(2*pi*3*f*t1)+sin(2*pi*4*f*t1)+sin(2*pi*5*f*t1);
figure;
plot(t1,s1);xlabel('time');ylabel('amplitude');title('HARMONICS');hold on;
stem(t1,s1);hold off;
Output :

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CONCLUSION:
After performing this practical we studied about sampling frequency, nyquist rate and
sampling theorem by plotting graph of sin wave.

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LAB. : 4 :SIGNAL OPERATIONS
Aim 1 : Perform the time shifting, amplitude scaling, folding operationon
discrete time signal.
Input :
%%%%%%%%% exp %%%%%%%%%
clc;
clearall;
closeall;
t=15;
x=exp(1:5);
plot(x);
v=shift(x,3,t);
f=fold(x);
s_f=amp_scaling(x,3);
%%%%%%%% fold %%%%%%%%%%
function v=fold(x)
k=size(x,2);
v=[];
fori=k:-1:1;
v=[v x(i)];
end
end
%%%%%%%% shift %%%%%%%%%
function v=shift(s,n,t)
if n>0
v=[zeros(1,n) s zeros(1,t-abs(n)-size(s,2))];
elseif n<0
v=[s zeros(1,t-size(s,2))];
else
v=[s zeros(1,t-size(s,2))];
end
end
end
%%%%%%% amp_scaling %%%%%%
function v= amp_scaling(s,scal_factor)
v=s*scal_factor

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%%%%%% code %%%%%
clc;
clearall;
closeall;
t=15;
x=exp(1:5);
plot(x);
v=shift(x,3,t);
f=fold(x);
s_f=amp_scaling(x,3);
figure;
subplot(2,2,1);plot(x);xlabel('time');ylabel('amplitude');title('exponatial');
subplot(2,2,2);plot(v);xlabel('time');ylabel('amplitude');title('shifting');
subplot(2,2,3);plot(f);xlabel('time');ylabel('amplitude');title('folding');
subplot(2,2,4);plot(s_f);xlabel('time');ylabel('amplitude');title('scaling');
Output:
Conclusion:
We Performed the time shifting, amplitude scaling, folding operation on discrete time signal.

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LAB. : 5 Generation of Continuous Time Domain Signals
Aim 1 : Recording of own voice and displaying its discrete samples
Software Required:
MATLAB 2013
Input:
% Record your voice for 5 seconds.
recObj = audiorecorder;
disp('Start speaking.')
recordblocking(recObj, 5);
disp('End of Recording.');
% Play back the recording.
play(recObj);
% Store data in double-precision array.
myRecording = getaudiodata(recObj);
% Plot the waveform.
plot(myRecording);
Output: Voice is recorded for 5 sec and the graph of the voice signal is obtained.

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Aim 2 : Recordand save voice file with .wavextension
Software Required:
MATLAB 2013
Input :
clc;
%input
Fs=8000;
ButtonName= questdlg('press start to record your sound',...
'record',...
'START','STOP','START' );
switch ButtonName,
case 'START'
x=wavrecord(60000,Fs);
msgbox('Now you can hear the recorded sound', 'play');
wavplay(10*x,Fs);
case 'STOP'
errordlg('you dont want to record??? ','???')
x=0;
end
wavwrite(x,Fs,'C:UsersArpit PatelDesktop');
x
Output :
Voice is recorded by clicking start button and recording is stopped by clicking stop button
and then recording is saved in .wav extension.
Aim 3 : Reading existing wave file
Software Required:
MATLAB 2013
Input :
%%%%%%%******program 5******%%%%%%
%processing of speech signal
[x,Fs]=wavread('C:UsersArpit PatelDownloadsMusica');

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n=1:length(x);
plot(n,x)
title('plot of a.wav')
xlabel('time')
ylabel('amplitude')
wavplay(x,Fs)
Output :
File is read from the destination and wave form is plotted as below.
Conclusion:
We studied about different MATLAB functions to record sound, play it, save it and plot its
waveform of the recorded or saved .wav file.

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LAB. : 6 Linearity
Aim 1 : Check linearity of the given function
Software Required:
MATLAB 2013
Input:
(a) y1(n)=2x(n)+3
x1=input(' enter input 1');
a1=input('weight of input 1');
Y11=2*(a1*x1+a2*x2)+3;
Y12=(2*(a1*x1)+3)+(2*(a2*x2)+3);
if Y11==Y12
disp('sys is linear ');
else
disp('sys is non-linear ');
end;
(b)
Y21=cos((a1*x1)+(a2*x2));
Y22=cos(a1*x1)+cos(a2*x2);
if Y21==Y22
disp('sys is linear ');
else
disp('sys is non-linear ');
end;

140953109008 Page32 EE A
output:
(a)
(b)
CONCLUSION:
We studied about linearity property and check linearity of the function using MATLAB.

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