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Basic simulation lab manual1
1. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
Siddharth Institute of Engineering and Technology
(Affiliated to J.N.T.UNIVERSITY, ANANTAPUR)
Narayanavanam, puttur, AP.
II YEAR BTECH I SEMESTER
BASIC SIMULATION LAB MANUAL
PREPARED BY:
VERIFIED BY:
LIST OF EXPERIMENTS
S.No Name of the Experiment
Basic operations on matrices.
1.
Generation on various signals and Sequences (periodic and a
periodic), such as unit impulse, unit step, square, saw tooth,
2.
triangular, sinusoidal, ramp, sinc.
Operations on signals and sequences such as addition,
multiplication, scaling, shifting, folding, computation of
3.
energy and average power.
Finding the even and odd parts of signal/sequence and real
4. and imaginary part of signal.
2. 5. Convolution between signals and sequences
Auto correlation and cross correlation between signals and
6. sequences.
Verification of linearity and time invariance properties of a
7. given continuous /discrete system.
Computation of unit sample, unit step and sinusoidal
response of the given LTI system and verifying its physical
8.
Reliability and stability properties.
Gibbs phenomenon.
9.
Finding the Fourier transform of a given signal and plotting
10.
its magnitude and phase spectrum
11. Waveform synthesis using Laplace Transform.
Locating the zeros and poles and plotting the pole zero maps
12. in s8plane and z8plane for the given transfer function.
Generation of Gaussian Noise (real and
complex),computation of its mean, M.S. Value and its skew,
13.
kurtosis, and PSD, probability distribution function.
14. Sampling theorem verification.
15. Removal of noise by auto correlation/cross correlation.
Extraction of periodic signal masked by noise using
16.
correlation.
17. Verification of Weiner8Khinchine relations.
18. Checking a random process for stationary in wide sense.
1
4. BASIC OPERATIONS ON MATRICES
Aim: To generate matrix and perform basic operation on matrices Using
MATLAB Software.
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
CONCLUSION:
EXP.NO: 2
GENERATION OF VARIOUS SIGNALS AND SEQUENCES (PERIODIC
AND APERIODIC), SUCH AS UNIT IMPULSE, UNIT STEP,
SQUARE, SAWTOOTH, TRIANGULAR, SINUSOIDAL, RAMP,
SINC.
Aim: To generate different types of signals Using MATLAB Software.
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000).
MATLAB Software
Matlab program:
%unit impulse
generation clc
close all
n1=-3;
n2=4;
n0=0;
n=[n1:n
2];
x=[(n-n0)==0]
stem(n,x)
% unit step
generation n1=-4;
n2=5;
n0=0;
9. xlabel('Time (sec)');ylabel('Amplitude'); title('Rectangular Aperiodic Pulse')
set(gcf,'Color',[1 1 1]),
%%To generate a rectangular pulse
t=-5:0.01:5;
pulse = rectpuls(t,2); %pulse of width 2 time units
plot(t,pulse)
axis([-5 5 -1 2]);
grid
10.
11. % sinusoidal signal
N=64; % Define Number of samples
n=0:N-1; % Define vector
n=0,1,2,3,...62,63 f=1000; % Define
the frequency
fs=8000; % Define the sampling
frequency x=sin(2*pi*(f/fs)*n); %
Generate x(t) plot(n,x); % Plot x(t) vs.
t
title('Sinewave [f=1KHz,
fs=8KHz]'); xlabel('Sample
Number'); ylabel('Amplitude');
% RAMP
clc
close all
n=input('enter the length of ramp');
t=0:n; plot(t); xlabel('t');
16. EXP.NO: 3
OPERATIONS ON SIGNALS AND SEQUENCES SUCH AS ADDITION,
MULTIPLICATION, SCALING, SHIFTING, FOLDING,
COMPUTATION OF ENERGY AND AVERAGE POWER
Aim: To perform arithmetic operations different types of signals Using
MATLAB Software.
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000).
MATLAB Softwar
%plot the 2 Hz sine wave in the top panel
t = [0:.01:1]; % independent (time) variable
A = 8; % amplitude
f1 = 2; % create a 2 Hz sine wave lasting
1 sec s1 = A*sin(2*pi*f1*t);
f2 = 6; % create a 4 Hz sine wave lasting
1 sec s2 = A*sin(2*pi*f2*t);
figure subplot(4,1,1) plot(t, s1)
title('1 Hz sine wave')
ylabel('Amplitude')
%plot the 4 Hz sine wave in the middle panel subplot(4,1,2)
plot(t, s2)
title('2 Hz sine wave')
ylabel('Amplitude')
%plot the summed sine waves in the bottom panel subplot(4,1,3)
plot(t, s1+s2) title('Summed sine waves') ylabel('Amplitude') xlabel('Time (s)')
xmult=s1.*s2;
subplot(4,1,4); plot(xmult); title('multiplication'); ylabel('Amplitude') xlabel('Time (s)')
20. 2. x(t)=3r(t-1)
3. x(t)=U(n+2-u(n-3)
4. x(n)=x1(n)+x2(n)where x1(n)={1,3,2,1},x2(n)={1,-2,3,2}
5. x(t)=r(t)-2r(t-1)+r(t-2)
6. x(n)=2δ(n+2)-2δ(n-4), -5≤ n ≥5.
7. X(n)={1,2,3,4,5,6,7,6,5,4,2,1} determine and plot the following
sequence a. x1(n)=2x(n-5-3x(n+4))
b. x2(n)=x(3-n)+x(n)x(n-
2)
CONCLUSION: Inthis experiment the various oprations on signals
have been performedUsing MATLAB have been demonstrated.
21. EXP.NO: 4
FINDING THE EVEN AND ODD PARTS OF SIGNAL/SEQUENCE AND
REAL AND IMAGINARY PART OF SIGNAL
Aim: program for finding even and odd parts of signals Using MATLAB
Software.
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000). MATLAB
Software
%even and odd signals program:
t=-4:1:4;
h=[ 2 1 1 2 0 1 2 2 3 ];
subplot(3,2,1)
stem(t,h);
xlabel('time'); ylabel('amplitude');
title('signal');
n=9;
22. for i=1:9 x1(i)=h(n); n=n-1;
end subplot(3,2,2)
stem(t,x1);
xlabel('time'); ylabel('amplitude');
title('folded
signal'); z=h+x1
subplot(3,2,3);
stem(t,z);
xlabel('time');
ylabel('amplitude'); title('sum
of two signal'); subplot(3,2,4);
stem(t,z/2);
xlabel('time'); ylabel('amplitude');
title('even
signal'); a=h-
x1;
subplot(3,2,5);
stem(t,a);
xlabel('time'); ylabel('amplitude');
title('difference of two signal');
subplot(3,2,6);
stem(t,a/2);
xlabel('time'); ylabel('amplitude');
title('odd signal');
23. % energy clc;
close all; clear all; x=[1,2,3]; n=3
e=0;
for i=1:n;
e=e+(x(i).*x(i));
end
% energy clc;
close all; clear all; N=2 x=ones(1,N) for i=1:N
y(i)=(1/3)^i.*x(i);
end n=N;
e=0;
for i=1:n;
e=e+(y(i).*y(i));
end
24. %
power
clc;
close all;
clear all;
N=2
x=ones(1,
N) for
i=1:N
y(i)=(1/3)^i.*x(i);
end
n=
N;
e=0
;
for i=1:n;
e=e+(y(i).*y(i))
;
end
p=e/(2*N+
1);
% power
N=input('type a value for
N'); t=-N:0.0001:N;
x=cos(2*pi*50*t).^2;
disp('the calculated power p of the
signal is'); P=sum(abs(x).^2)/length(x)
plot(t,x);
axis([0 0.1 0 1]);
disp('the theoretical power of the
signal is'); P_theory=3/8
CONCLUSION:
25. EXP.NO:
5 LINEAR CONVOLUTION
Aim: To find the out put with linear convolution operation Using MATLAB
Software.
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000). MATLAB
Software
Program:
clc;
close all;
clear all;
x=input('enter input
sequence'); h=input('enter
impulse response');
y=conv(x,h);
subplot(3,1,1);
stem(x);
xlabel('n');ylabel('x(n)'
); title('input signal')
subplot(3,1,2);
stem(h);
xlabel('n');ylabel('h(n)'
); title('impulse
response')
subplot(3,1,3);
28. EXP.NO: 6
6. AUTO CORRELATION AND CROSS CORRELATION BETWEEN
SIGNALS AND SEQUENCES.
………………………………………………………………………………………………
Aim: To compute auto correlation and cross correlation between signals and
sequences
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000). MATLAB
Software
% Cross
Correlation clc;
close all;
clear all;
x=input('enter input sequence');
h=input('enter the impulse suquence');
subplot(3,1,
1); stem(x);
xlabel('n');
ylabel('x(n)');
title('input signal');
subplot(3,1,
2); stem(h);
xlabel('n');
ylabel('h(n)');
title('impulse
signal');
y=xcorr(x,h);
subplot(3,1,3);
stem(y);
xlabel('n');
ylabel('y(n)');
disp('the resultant signal is');
disp(y);
title('correlation signal');
29.
30. % auto
correlation clc;
close all;
clear all;
x = [1,2,3,4,5]; y = [4,1,5,2,6];
subplot(3,1,
1); stem(x);
xlabel('n');
ylabel('x(n)');
title('input
signal');
subplot(3,1,2);
stem(y);
xlabel('n');
ylabel('y(n)');
title('input
signal');
z=xcorr(x,x);
subplot(3,1,3);
stem(z);
xlabel('n');
ylabel('z(n)');
title('resultant signal signal');
31. CONCLUSION: In this experiment correlation of various signals
have been performed Using MATLAB
Applications:it is used to measure the degree to which the two signals are
similar and it is also used for radar detection by estimating the time delay.it
is also used in Digital communication, defence applications and sound
navigation
Excersize questions: perform convolution between the following signals
1. X(n)=[1 -1 4 ], h(n) = [ -1 2 -3 1]
2. perform convolution between the. Two periodic
sequences x1(t)=e-3t{u(t)-u(t-2)} , x2(t)= e -3t
for 0 ≤ t ≤ 2
32. EXP.NO: 7
VERIFICATION OF LINEARITY AND TIME INVARIANCE PROPERTIES OF A
GIVEN CONTINUOUS /DISCRETE SYSTEM.
Aim: To compute linearity and time invariance properties of a given continuous
/discrete system
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
Program1:
clc;
clear all;
close all;
n=0:40; a=2; b=1;
x1=cos(2*pi*0.1*n);
x2=cos(2*pi*0.4*n);
x=a*x1+b*x2; y=n.*x;
y1=n.*x1;
y2=n.*x2;
yt=a*y1+b*y2;
33. d=y-yt;
d=round(
d) if d
disp('Given system is not satisfy linearity property');
else
disp('Given system is satisfy linearity property');
end
subplot(3,1,1), stem(n,y);
grid subplot(3,1,2),
stem(n,yt); grid
subplot(3,1,3), stem(n,d);
grid
Program2:
clc;
clear all;
close all;
n=0:40; a=2; b=-
3;
x1=cos(2*pi*0.1*n)
;
x2=cos(2*pi*0.4*n)
; x=a*x1+b*x2;
y=x.^2;
y1=x1.^2;
y2=x2.^2;
yt=a*y1+b*y2
;
34. d=y-yt;
d=round(d
); if d
disp('Given system is not satisfy linearity property');
else
disp('Given system is satisfy linearity property');
end
subplot(3,1,1), stem(n,y); grid
subplot(3,1,2), stem(n,yt); grid
subplot(3,1,3), stem(n,d); grid
Program
clc;
close all;
clear all;
x=input('enter the sequence');
N=length(x);
n=0:1:N-1;
39. EXP.NO:8
COMPUTATION OF UNIT SAMPLE, UNIT STEP AND SINUSOIDAL
RESPONSE OF THE GIVEN LTI SYSTEM AND VERIFYING ITS
PHYSICAL REALIZABILITY AND STABILITY PROPERTIES.
Aim: To Unit Step And Sinusoidal Response Of The Given LTI System And
Verifying
Its Physical Realizability And Stability
Properties.
EQUIPMENTS:
PC with windows
(95/98/XP/NT/2000).
MATLAB
Software
%calculate and plot the impulse response and step
response b=[1];
a=[1,-1,.9];
x=impseq(0,-20,120); n = [-20:120]; h=filter(b,a,x); subplot(3,1,1);stem(n,h);
title('impulse response'); xlabel('n');ylabel('h(n)');
=stepseq(0,-20,120); s=filter(b,a,x); s=filter(b,a,x); subplot(3,1,2); stem(n,s);
title('step response'); xlabel('n');ylabel('s(n)') t=0:0.1:2*pi;
x1=sin(t);
%impseq(0,-20,120); n = [-20:120]; h=filter(b,a,x1); subplot(3,1,3);stem(h);
title('sin response'); xlabel('n');ylabel('h(n)'); figure;
zplane(b,a);
42. EXP.NO: 9 GIBBS PHENOMENON
Aim: To verify the Gibbs Phenomenon.
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
Gibbs Phenomina Program :
t=0:0.1:(pi*8); y=sin(t); subplot(5,1,1); plot(t,y); xlabel('k');
ylabel('amplitude'); title('gibbs phenomenon'); h=2;
%k=3;
for k=3:2:9 y=y+sin(k*t)/k; subplot(5,1,h);
plot(t,y); xlabel('k'); ylabel('amplitude'); h=h+1;
end
43. CONCLUSION: In this experiment Gibbs phenomenon have been
demonstrated Using MATLAB
44. EXP.NO: 10.
FINDING THE FOURIER TRANSFORM OF A GIVEN SIGNAL AND
PLOTTING ITS MAGNITUDE AND PHASE SPECTRUM
Aim: to find the fourier transform of a given signal and plotting its
magnitude and phase spectrum
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
45. MATLAB Software
Program:
clc;
close all;
clear all;
x=input('enter the sequence'); N=length(x);
n=0:1:N-1; y=fft(x,N) subplot(2,1,1); stem(n,x);
title('input sequence'); xlabel('time index n----->'); ylabel('amplitude x[n]-
---> '); subplot(2,1,2);
stem(n,y);
title('output sequence');
xlabel(' Frequency index K---->');
ylabel('amplitude X[k]------>');
46. FFT magnitude and Phase plot:
clc
close all x=[1,1,1,1,zeros(1,4)]; N=8;
X=fft(x,N); magX=abs(X),phase=angle(X)*180/pi; subplot(2,1,1)
plot(magX); grid xlabel('k')
ylabel('X(K)') subplot(2,1,2) plot(phase);
48. CONCLUSION: In this experiment the fourier transform of a given signal
and plotting its magnitude and phase spectrum have been demonstrated
using matlab
49. Exp:11
LAPLACE TRNASFORMS
Aim: To perform waveform synthesis using Laplece Trnasforms of a given
signal
Program for Laplace Transform:
f=t
syms f t; f=t; laplace(f)
Program for nverse Laplace Transform
f(s)=24/s(s+8) invese LT
syms F s F=24/(s*(s+8)); ilaplace(F)
y(s)=24/s(s+8) invese LT poles and zeros
52. CONCLUSION: In this experiment the Triangular signal synthesised using
Laplece Trnasforms using MATLAB
53. EXP.NO: 12
LOCATING THE ZEROS AND POLES AND PLOTTING THE POLE ZERO
MAPS IN S-PLANE AND Z-PLANE FOR THE GIVEN TRANSFER FUNCTION.
Aim: To locating the zeros and poles and plotting the pole zero maps in
s-plane and z- plane for the given transfer function
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
clc; close all clear all;
%b= input('enter the numarator cofficients')
%a= input('enter the denumi cofficients')
b=[1 2 3 4] a=[1 2 1 1 ] zplane(b,a);
Result: :
54. EXP.NO: 13
13. Gaussian noise
%Estimation of Gaussian density and Distribution Functions
%% Closing and Clearing
all clc;
clear all;
close all;
%% Defining the range for the Random
variable dx=0.01; %delta x
x=-3:dx:3; [m,n]=size(x);
%% Defining the parameters of the pdf
mu_x=0; % mu_x=input('Enter the value of mean');
sig_x=0.1; % sig_x=input('Enter the value of varience');
%% Computing the probability density
function px1=[];
a=1/(sqrt(2*pi)*sig_x);
for j=1:n
px1(j)=a*exp([-((x(j)-mu_x)/sig_x)^2]/2);
end
%% Computing the cumulative distribution
function cum_Px(1)=0;
for j=2:n
cum_Px(j)=cum_Px(j-1)+dx*px1(j);
end
%% Plotting the
results figure(1)
plot(x,px1);grid
axis([-3 3 0 1]);
title(['Gaussian pdf for mu_x=0 and sigma_x=', num2str(sig_x)]);
xlabel('--> x')
ylabel('--> pdf')
figure(2)
plot(x,cum_Px);gri
d axis([-3 3 0 1]);
title(['Gaussian Probability Distribution Function for mu_x=0 and
sigma_x=', num2str(sig_x)]);
title('ite^{omegatau} = cos(omegatau) + isin(omegatau)')
xlabel('--> x')
ylabel('--> PDF')
55. EXP.NO: 14
14. Sampling theorem verification
Aim: To detect the edge for single observed image using sobel edge detection
and canny edge detection.
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
56. Figure 2: (a) Original signal g(t) (b) Spectrum G(w)
δ (t) is the sampling signal with fs = 1/T > 2fm.
Figure 3: (a) sampling signal δ (t) ) (b) Spectrum δ (w)
Let gs(t) be the sampled signal. Its Fourier Transform Gs(w) isgiven by
Figure 4: (a) sampled signal gs(t) (b) Spectrum Gs(w)
57. To recover the original signal G(w):
1. Filter with a Gate function, H2wm(w) of width 2wm
Scale it by T.
Figure 5: Recovery of signal by filtering with a fiter of width 2wm
Aliasing
{ Aliasing is a phenomenon where the high frequency components of the
sampled signal interfere with each other because of inadequate sampling
ws < 2wm.
Figure 6: Aliasing due to inadequate sampling
58. Aliasing leads to distortion in recovered signal. This is the
reason why sampling frequency should be atleast twice thebandwidth of
the signal. Oversampling
{ In practice signal are oversampled, where fs is
signi_cantly higher than Nyquist rate to avoid
aliasing.
Figure 7: Oversampled signal-avoids aliasing t=-10:.01:10;
T=4; fm=1/T; x=cos(2*pi*fm*t); subplot(2,2,1); plot(t,x);
xlabel('time');ylabel('x(t)') title('continous time signal') grid;
n1=-4:1:4 fs1=1.6*fm; fs2=2*fm; fs3=8*fm;
x1=cos(2*pi*fm/fs1*n1); subplot(2,2,2); stem(n1,x1); xlabel('time');ylabel('x(n)')
title('discrete time signal with fs<2fm')
hold on subplot(2,2,2); plot(n1,x1) grid;
n2=-5:1:5; x2=cos(2*pi*fm/fs2*n2); subplot(2,2,3); stem(n2,x2);
xlabel('time');ylabel('x(n)')
title('discrete time signal with fs=2fm')
hold on
subplot(2,2,3); plot(n2,x2) grid;
n3=-20:1:20;
59.
60. x3=cos(2*pi*fm/fs3*n
3); subplot(2,2,4);
stem(n3,x3);
xlabel('time');ylabel('x(
n)')
title('discrete time signal with fs>2fm')
hold on
subplot(2,2
,4);
plot(n3,x3)
grid;
CONCLUSION: In this experiment the sampling theorem have been verified
Using MATLAB
65. subplot(7,1,1)
plot(s);
title('signal s');xlabel('t');ylabel('amplitude');
c=cos(t); subplot(7,1,2) plot(c);
title('signal c');xlabel('t');ylabel('amplitude');
n = randn([1 126]); f=s+n; subplot(7,1,3) plot(f);
title('signal f=s+n');xlabel('t');ylabel('amplitude');
asc=xcorr(s,c); subplot(7,1,4) plot(asc);
title('auto correlation of s and c');xlabel('t');ylabel('amplitude');
anc=xcorr(n,c); subplot(7,1,5) plot(anc);
title('auto correlation of n and c');xlabel('t');ylabel('amplitude');
cfc=xcorr(f,c); subplot(7,1,6) plot(cfc);
title('auto correlation of f and c');xlabel('t');ylabel('amplitude');
hh=asc+anc; subplot(7,1,7) plot(hh);
title('addition of asc+anc');xlabel('t');ylabel('amplitude');
76
68. EXP.No:16
Program:
EXTRACTION OF
Clear all; close all; clc; n=256; k1=0:n-1;
P
x=cos(32*pi*k1/n)+sin(48*pi*k1/n);
E
plot(k1,x)
R
%Module to find period of input signl k=2;
I
xm=zeros(k,1); ym=zeros(k,1); hold on
O
for i=1:k
D
[xm(i) ym(i)]=ginput(1);
I
plot(xm(i), ym(i),'r*');
C
end
period=abs(xm(2)-xm(1)); rounded_p=round(period);
S
m=rounded_p
I
% Adding noise and plotting noisy signal
G
N
A
L
M
A
y=x+randn(1,n);
S
figure plot(k1,y)
K
E
D
B
Y
N
O
I
S
E
U
S
I
N
G
C
O
R
R
E
L
A
T
I
O
N
Extraction of
Periodic Signal
Masked By Noise
Using
Correlation
69. % To generate impulse train with the period as that of input signal
d=zeros(1,n);
for i=1:n
if (rem(i-1,m)==0)
d(i)=1;
end end
%Correlating noisy signal and impulse train cir=cxcorr1(y,d);
%plotting the original and reconstructed signal m1=0:n/4;
figure
Plot (m1,x(m1+1),'r',m1,m*cir(m1+1));
70.
71. CONCLUSION: In this experiment the Weiner-Khinchine Relation have
been verified using MATLAB.
72. EXP.No:17
VERIFICATION OF WIENER–KHINCHIN RELATION
AIM: Verification of wiener–khinchine relation
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
PROGRAM:
Clc
clear all;
t=0:0.1:2*pi; x=sin(2*t); subplot(3,2,1); plot(x); au=xcorr(x,x); subplot(3,2,2);
plot(au); v=fft(au); subplot(3,2,3); plot(abs(v)); fw=fft(x); subplot(3,2,4);
plot(fw);
fw2=(abs(fw)).^2;
subplot(3,2,5); plot(fw2);
Result:
73. EXP18.
CHECKING A RANDOM PROCESS FOR STATIONARITY IN WIDE SENSE.
AIM: Checking a random process for stationary in wide sense.
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
MATLAB PROGRAM:
Clear all
Clc
y = randn([1 40]) my=round(mean(y));
z=randn([1 40]) mz=round(mean(z)); vy=round(var(y)); vz=round(var(z));
t = sym('t','real'); h0=3; x=y.*sin(h0*t)+z.*cos(h0*t); mx=round(mean(x));
k=2;
xk=y.*sin(h0*(t+k))+z.*cos(h0*(t+k));
x1=sin(h0*t)*sin(h0*(t+k));
x2=cos(h0*t)*cos(h0*(t+k)); c=vy*x1+vz*x1;
% if we solve “c=2*sin (3*t)*sin (3*t+6)" we get c=2cos (6)
% which is a costant does not depent on variable’t’
% so it is wide sence stationary
Result:
