19A017
JATIN KATIYAR
SIGNAL AND SYSTEMS LAB
NO 6-7
JATIN KATIYAR 191A017
[191𝐴017]
CODE
% Program for signal synthesis using TFS
clc;
clear all;
T=2*pi; %Time period of the waveform
N=100; %Number of harmonics
t=0:0.01:3*T; %Plotting range of signal
a0=pi/2; %Average value of signal
w0=1;
191A017
JATIN KATIYAR 191A017
d_sin=[];d_cos=[];
for n=1:2:N %For EFS range is –N to N with suitable
interval
an=-4/(n^2*pi); %Cosine coefficients
bn=0; %Sine coefficients
a_cos = an*cos(n*w0*t); %Cosine components
b_sin = bn*sin(n*w0*t); %Sine components
d_cos = [d_cos;a_cos];
d_sin = [d_sin;b_sin];
end
x=a0+sum(d_cos)+sum(d_sin); %Fourier series for signal x(t)
subplot(333)
plot(t,d_cos) %Plot for cosine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Cosine components of waveforms')
subplot(336)
plot(t,d_sin) %Plot for sine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Sine components of waveforms')
subplot(339)
plot(t,x) %Plot for waveform
xlabel('time t --->')
ylabel('Amplitude --->')
title('Synthesized waveform using Fourier series');
ANS
GRAPH
[191𝐴017]
191A017
JATIN KATIYAR 191A017
CODE
% Program for signal synthesis using TFS
clc;
clear all;
T=2*pi; %Time period of the waveform
N=120; %Number of harmonics
t=0:0.01:4*T; %Plotting range of signal
a0=(1-exp(-2*pi))/2*pi; %Average value of signal
191A017
JATIN KATIYAR 191A017
w0=1;
d_sin=[];d_cos=[];
for n=1:2:N %For EFS range is –N to N with suitable
interval
an=(1-exp(-2*pi))/((n^2+1)*pi); %Cosine coefficients
bn=((1-exp(-2*pi))*n)/((n^2+1)*pi); %Sine coefficients
a_cos = an*cos(n*w0*t); %Cosine components
b_sin = bn*sin(n*w0*t); %Sine components
d_cos = [d_cos;a_cos];
d_sin = [d_sin;b_sin];
[191𝐴017]
end
x=a0+sum(d_cos)+sum(d_sin); %Fourier series for signal x(t)
subplot(333)
plot(t,d_cos) %Plot for cosine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Cosine components of waveforms')
subplot(336)
plot(t,d_sin) %Plot for sine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Sine components of waveforms')
subplot(339)
plot(t,x) %Plot for waveform
xlabel('time t --->')
ylabel('Amplitude --->')
title('Synthesized waveform using Fourier series');
ANS
GRAPH
[191𝐴017]
191A017
JATIN KATIYAR 191A017
CODE
% Program for signal synthesis using TFS
clc;
clear all;
T=8; %Time period of the waveform
N=120; %Number of harmonics
t=0:0.01:5*T; %Plotting range of signal
a0=16/3;; %Average value of signal
w0=2*pi/4;
d_sin=[];d_cos=[];
for n=1:2:N %For EFS range is –N to N with suitable
interval
191A017
JATIN KATIYAR 191A017
an=(64*power(-1,n))/(( pi^2)*(n^2)); %Cosine coefficients
bn=0; %Sine coefficients
a_cos = an*cos(n*w0*t); %Cosine components
b_sin = bn*sin(n*w0*t); %Sine components
d_cos = [d_cos;a_cos];
d_sin = [d_sin;b_sin];
end
x=a0+sum(d_cos)+sum(d_sin); %Fourier series for signal x(t)
subplot(333)
plot(t,d_cos) %Plot for cosine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Cosine components of waveforms')
subplot(336)
plot(t,d_sin) %Plot for sine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Sine components of waveforms')
subplot(339)
plot(t,x) %Plot for waveform
xlabel('time t --->')
ylabel('Amplitude --->')
title('Synthesized waveform using Fourier series');
ANS
GRAPH
[191𝐴017]
191A017
JATIN KATIYAR 191A017
[191𝐴017]
CODE
% Program for signal synthesis using TFS
clc;
clear all;
T=4; %Time period of the waveform
191A017
JATIN KATIYAR 191A017
N=200; %Number of harmonics
t=0:0.01:3*T; %Plotting range of signal
a0=0; %Average value of signal
w0=pi/2;
d_sin=[];d_cos=[];
for n=1:2:N %For EFS range is –N to N with suitable
interval
an=sin((n*pi)/6).*sin((n*pi)/2).*sin((n*pi)/3).*(8/(n*pi));
%Cosine coefficients
bn=sin((n*pi)/6).*sin((n*pi)/2).*cos((n*pi)/3).*(8/(n*pi));
%Sine coefficients
a_cos = an*cos(n*w0*t); %Cosine components
b_sin = bn*sin(n*w0*t); %Sine components
d_cos = [d_cos;a_cos];
d_sin = [d_sin;b_sin];
end
x=a0+sum(d_cos)+sum(d_sin); %Fourier series for signal x(t)
subplot(333)
plot(t,d_cos) %Plot for cosine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Cosine components of waveforms')
subplot(336)
plot(t,d_sin) %Plot for sine components
xlabel('time t --->')
ylabel('Amplitude --->')
title('Sine components of waveforms')
subplot(339)
plot(t,x) %Plot for waveform
xlabel('time t --->')
ylabel('Amplitude --->')
title('Synthesized waveform using Fourier series');
ANS
191A017
JATIN KATIYAR 191A017
GRAPH
[191𝐴017]
191A017
JATIN KATIYAR 191A017
CODE
clc;
clear all;
N=100;
T=10;
t=0:0.001:3*T;
w0=(2*pi)/T;
d_exp=[];
for n=-N:1:N
cn=1/((n+eps)*pi)*(sin(n*pi/5)*exp((-j*n*pi)/5));
c_exp=cn*exp(j*w0*n*t);
d_exp=[d_exp;c_exp];
end
c0=1/5;
x=c0+sum(d_exp);
subplot(2,1,1);
plot(t,d_exp);
xlabel('time t---->');
ylabel('amplitude');
title('component of wave');
subplot(2,1,2);
plot(t,x);
xlabel('time t---->');
ylabel('amplitude');
title('component of x');
[191𝐴017]
ANS
GRAPH
191A017
JATIN KATIYAR 191A017
[191𝐴017]
191A017
JATIN KATIYAR 191A017
[191𝐴017]
CODE
syms t s;
h=exp(-2*t)+2*t*exp(-t)-exp(-t);
x1=laplace(h,t,s)
y=simplify(x1)
ANS
nuntitled2
x1 =
2/(s + 1)^2 - 1/(s + 1) + 1/(s + 2)
191A017
JATIN KATIYAR 191A017
y =
(s + 3)/((s + 1)^2*(s + 2))
N=[1,3];
D=[1,4,5,2];
roots(N)
[191𝐴017]
ans =
-3
roots(D)
ans =
-2.0000 + 0.0000i
-1.0000 + 0.0000i
-1.0000 - 0.0000i
pzmap(roots(D),roots(N))
stable
GRAPH
191A017
JATIN KATIYAR 191A017
CODE
syms t s
x=((s+3)/s^3+5*s^2+12*s+8);
ilaplace(x)
simplify(x)
N=[1,3]; %Numerator coefficients
D=[1,5,12,8]; %denominator coefficients
[r, p, k]=residue(N, D)
factor(s^3+5*s^2+12*s+8)
ANS
nuntitled2
ans =
t + 8*dirac(t) + (3*t^2)/2 + 12*dirac(1, t) + 5*dirac(2, t)
ans =
12*s + (s + 3)/s^3 + 5*s^2 + 8
r =
-0.2000 - 0.1500i
-0.2000 + 0.1500i
0.4000 + 0.0000i
p =
-2.0000 + 2.0000i
-2.0000 - 2.0000i
-1.0000 + 0.0000i
k =
[]
ans =
[s + 1, s^2 + 4*s + 8]
191A017
JATIN KATIYAR 191A017
CODE
yms t s
x=((s^3+8*s^2+24*s+32)/(s^2+6*s+8));
ilaplace(x)
[191𝐴017]
simplify(x)
N=[1,3]; %Numerator coefficients
D=[1,5,12,8]; %denominator coefficients
[r, p, k]=residue(N, D)
factor((s^2+6*s+8))
roots(N)
roots(D)
% Pole-zero diagram/map
pzmap(roots(D),roots(N))
ANS
nuntitled2
ans =
4*exp(-2*t) + 2*dirac(t) + dirac(1, t)
ans =
(s^2 + 4*s + 8)/(s + 2)
r =
-0.2000 - 0.1500i
-0.2000 + 0.1500i
0.4000 + 0.0000i
p =
-2.0000 + 2.0000i
-2.0000 - 2.0000i
-1.0000 + 0.0000i
k =
191A017
JATIN KATIYAR 191A017
[]
ans =
[s + 4, s + 2]
ans =
-3
ans =
-2.0000 + 2.0000i
-2.0000 - 2.0000i
-1.0000 + 0.0000i
GRAPH
191A017
JATIN KATIYAR 191A017
CODE
% Fourier transform
syms t w
tau = 1;
trig =triangularPulse(t) % generation of tri(t/2tau)
trig_FT = fourier(trig) % Fourier Transform rect(t/tau)
t_v= (-3:0.01:3);
trig_t = subs(trig, t, t_v+eps);
% subs( ) to get the numericaltrig(t/2tau)
subplot(2,1,1);
plot(t_v, trig_t); % plot of rectangular pulse
axis([-3 3 -0.1 1.1]);
xlabel('t sec');ylabel('x(t)');
title('triangular Pulse of width 2')
w_v = (-20:0.01:20);
trig_w = subs(trig_FT, w, w_v+eps);
%subs()to get the numerical value of FT
subplot(2, 1, 2);
plot(w_v, abs(trig_w), w_v, angle(trig_w) );%magnitude and phase spectrum
legend('Magnitude spectrum','Phase spectrum')
xlabel('\omega (rad/s)');ylabel('X(\omega)')
title('Sinc Pulse of width 2\pi')
ANS
jatinkatiyaruntitled2
trig_FT =
-(exp(-w*1i)*(exp(w*1i) - 1)^2)/w^2
GRAPH
[191𝐴017]
191A017
JATIN KATIYAR 191A017
USING HEAVISIDE FUNCTION (JATIN KATIYAR 191A017)
% Fourier transform
syms t w
tau = 1;
trig =(t+tau).*heaviside(t+tau)-2*(t).*heaviside(t)+(t-tau).*heaviside(t-tau); %
generation of tri(t/2tau)
trig_FT = fourier(trig) % Fourier Transform rect(t/tau)
t_v= (-3:0.01:3);
trig_t = subs(trig, t, t_v+eps);
% subs( ) to get the numericaltrig(t/2tau)
subplot(2,1,1);
plot(t_v, trig_t); % plot of rectangular pulse
axis([-3 3 -0.1 1.1]);
xlabel('t sec');ylabel('x(t)');
title('triangular Pulse of width 2')
w_v = (-20:0.01:20);
trig_w = subs(trig_FT, w, w_v+eps);
%subs()to get the numerical value of FT
subplot(2, 1, 2);
plot(w_v, abs(trig_w), w_v, angle(trig_w) );%magnitude and phase spectrum
legend('Magnitude spectrum','Phase spectrum')
xlabel('\omega (rad/s)');ylabel('X(\omega)')
title('Sinc Pulse of width 2\pi')
ANS
jatinkatiyaruntitled2
191A017
JATIN KATIYAR 191A017
trig_FT =
2/w^2 + exp(-w*1i)*(pi*dirac(1, w) + 1i/w^2)*1i + exp(w*1i)*(pi*dirac(1, w) + 1i/w^2)*1i - pi*dirac(1, w)*2i
GRAPH
191A017
CODE
[191𝐴017]
syms t w
191A017
JATIN KATIYAR 191A017
x= t*exp(-t^2);
r=5*sinc((5*t)/pi)+10*sinc((10*t)/pi);
X=fourier(x,w)
R=fourier(r,w)
Y=ifourier(X,t)
S=ifourier(R,t)
subplot(2,2,1);
ezplot(X,w);
subplot(2,2,2);
ezplot(Y,t);
subplot(2,2,3);
ezplot(R,w);
Y=ifourier(X,t)
subplot(2,2,4);
ezplot(S,t);
ANS
GRAPH
191A017
SIGNALS AND SYSTEMS
Lab -03
191A017
jatin katiyar
191A017 JATIN KATIYAR
[191𝐴017]
close all;
n=-10:10;
x1=impseq(0,-10,10)+2*impseq(2,-10,10)+3*impseq(-3,-10,10);
x2=impseq(0,-10,10)+2*impseq(2,-10,10)-6*impseq(-2,10,10)+8*impseq(7,-10,10)-5*impseq(-5,-10,10);
subplot(2,2,1);
stem(n,x1);grid on;
xlabel('discrete n');
xlabel('discrete signal');
title('exercise 1(a)');
subplot(2,2,2);
stem(n,x2);grid on;
xlabel('discrete n');
xlabel('discrete signal');
title('exercise 1(b)');
191A017
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
[191𝐴017]
n=-12:12;
x1=stepseq(5,-12,12)-stepseq(11,-12,12)+2*stepseq(-8,12,12)-2*stepseq(2,-12,12);
x2=n.^2.*(stepseq(-5,-12,12)-2*stepseq(6,12,12))+10*stepseq(0,-12,12)+20*(0.5).^n.*(stepseq(4,12,12)-stepseq(10,-12,12));
subplot(2,2,1);
stem(n,x1);grid on;
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
xlabel('discrete n');
[191𝐴017]
xlabel('discrete signal');
title('exercise 1(a)');
subplot(2,2,2);
stem(n,x2);grid on;
xlabel('discrete n');
xlabel('discrete signal');
title('exercise 1(b)');
191A017 JATIN KATIYAR
191A017
191A017 JATIN KATIYAR
n=-12:12;
x1=-impseq(-1,-12,12)-2*impseq(-2,-12,12)-3*impseq(-3,12,12)-4*impseq(-4,-12,12)-5*impseq(-5,-12,12)+impseq(1,12,12)+2*impseq(2,-12,12)+3*impseq(3,-12,12)+4*impseq(4,12,12)+5*impseq(5,-12,12);
subplot(2,2,1);
stem(n,x1);grid on;
191A017
xlabel('discrete n');
xlabel('discrete signal');
title('exercise 3)');
% subplot(2,2,2);
% stem(n,x2);grid on;
% xlabel('discrete n');
% xlabel('discrete signal');
% title('exercise 1(b)');
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
n=-12:12;
x1=impseq(-8,-12,12)+impseq(-7,-12,12)+impseq(-6,12,12)+impseq(-5,-12,12)+impseq(-4,-12,12)+impseq(-3,12,12)+2*impseq(-2,-12,12)+3*impseq(-1,-12,12)+4*impseq(0,12,12)+3*impseq(1,-12,12)+2*impseq(2,-12,12)+impseq(3,12,12)+impseq(4,-12,12)+impseq(5,-12,12)+impseq(6,12,12)+impseq(7,-12,12)+impseq(8,-12,12);
x2=stepseq(-8,-12,12)+stepseq(-2,-12,12)+stepseq(-1,12,12)+stepseq(0,-12,12)-stepseq(1,-12,12)-stepseq(2,12,12)-stepseq(3,-12,12)-stepseq(9,-12,12);
subplot(2,2,1);
stem(n,x1,'r');grid on;
xlabel('distance time n');
xlabel('discrete signal');
title('exercise 4');
% subplot(2,2,2);
hold on;
stem(n,x2,'g');grid on;
legend('x1','x2');
xlabel('discrete n');
191A017
xlabel('discrete signal');
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
title('exercise 1(b)');
subplot(2,2,3);
stem(n,x1,'r');grid on;
xlabel('distance time n');
xlabel('discrete signal');
title('exercise 4');
subplot(3,3,1);
stem(n,x2,'g');grid on;
legend('x1','x2');
xlabel('discrete n');
xlabel('discrete signal');
title('exercise 1(b)');
191A017
close all;
n=-30:30;
x1=n.*stepseq(10,-30,30)-n.*stepseq(0,-30,30);
x2=15*(exp(-n+10).*(n.*stepseq(10,-30,30)-n.*stepseq(20,30,30) );
x3=20*cos(0.1*pi*n).*(n.*stepseq(20,-30,30)-n.*stepseq(30,30,30) );
plot(n,x1);grid on;
xlabel('time n');
ylabel('discrete signal');
title('exercise 5)');
hold on;
plot(n,x1);grid on;
xlabel('time n');
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
ylabel('discrete signal');
title('exercise 5');
hold on;
plot(n,x1);grid on;
xlabel('time n ');
ylabel('discrete signal');
title('exercise 5');
hold on;
legend('x1','x2','x3');
191A017 JATIN KATIYAR
LAB NO.2
(191A017)
jatin katiyar
JATIN KATIYAR 191A017
[191𝐴017]
Code
(a)close all;
clc;
t=0:0.01:0.99;
y=4*cos((5*pi*t)-(pi/4));
plot(t,y)
xlabel('continous time t');
[191𝐴017]
ylabel('amplitude');
title('cosine function','fontsize',12)
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
(b)t=-1.5:(3.5/99):2;
y=cos(4*t)-2*sin(8*t);
plot(t,y);
xlabel('continous time t');
ylabel('amplitude');
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
(a)n=linspace(0,1,100);
y=4*cos(0.1*n*pi);
grid on;
stem(n,y);
xlabel('discrete plot');
ylabel('amplitude');
title('cosine plot','fontsize',12);
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
(b)
t=linspace(0,0.99,100);
w=linspace(-10,10,100);
y=5*exp(-j*w.*t);
y1=real(y);
y2=imag(y);
subplot(2,2,1);
plot(t,y1,t,y2);
grid on;
xlabel('continuoes time t');
ylabel('Amplitude');
title('Exponential Function')
legend('y2 Imagenary','y1 real');
subplot(2,2,2);
plot3(t,w,y); grid on;
xlabel('continuoes time t');
ylabel('Amplitude');
title('3-d Exponential Function')
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
t=-1:6/599:5;
y=(exp(-2*t)).*(cos(6*pi*t));
%subplot(2,2,1);
figure(1);
plot(t,y);
xlabel('t sec');
ylabel('f(t) volts');
axis([-2, 7, -10, 10]);
n=-1:6/599:5;
y=(exp(-2*n)).*(cos(6*pi*n));
%subplot(2,2,2);
figure(2);
stem(t,y);
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
xlabel('t sec');
ylabel('f(t) volts');
axis([-2, 7, -10, 10]);
[191𝐴017]
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
t=-1:6/599:5;
y=(exp(-2*t)).*(cos(6*pi*t));
subplot(2,2,1);
% figure(1);
plot(t,y);
xlabel('t sec');
ylabel('f(t) volts');
axis([-2, 7, -10, 10]);
title('difference between plot and stem');
n=-1:6/599:5;
y=(exp(-2*n)).*(cos(6*pi*n));
subplot(2,2,2);
% figure(2);
stem(t,y);
xlabel('t sec');
ylabel('f(t) volts');
axis([-2, 7, -10, 10]);
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
t1=-8:-3;
x1=0+t1*0;
t2=-4:2;
x2=(t2+2)+t2*0;
t3=3:8;
x3=(t3-2)+t3*0;
t=[t1 t2 t3];
x=[x1 x2 x3];
plot(t,x)
xlabel('t sec');
ylabel('x(t) volts');
title('exercise 4');
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
n1=-8:-3;
x1=0+n1*0;
n2=-4:2;
x2=(n2+2)+n2*0;
n3=3:8;
x3=(n3-2)+n3*0;
n=[n1 n2 n3];
x=[x1 x2 x3];
stem(n,x)
xlabel('n sec');
ylabel('x(n) volts');
title('exercise 4');
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
[191𝐴017]
t1=0:10;
x1=-20+4*t;
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
t2=10:20;
x2=20+t2*0;
t3=20:23;
x3= 9.74.*10^9.*exp(-t3)+t3*0;
x=[x1,x2,x3];
t=[t1 t2 t3];
plot(t,x);grid on;
xlabel('time');
ylabel('continous signal');
axis([-3 30 -5 30]);
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
Signals & Systems Lab: Experiment # 4
191A017
JATIN KATIYAR
191A017 JATIN KATIYAR
[191𝐴017]
Code with user define function
n=-3:4;
x= [1, 1,-3, 4, 6,-5,8,10];
subplot(3,2,1);
stem(n,x);
x2=sigfold(5*x,n);
subplot(3,2,2);
stem(n,x2);
x3=sigshift(3*x,n,-2);
subplot(3,2,3);
stem(n-2,x3);grid on;
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
subplot(3,2,4);
x4=sigfold(-2*x3,n);
stem(n+1,x4);grid on;
signfold.m function
function [y,n]=sigfold(x,m);
n=-fliplr(m);
[191𝐴017]
y=fliplr(x);
signshift.m function
function [y,n]=sigshift(x,m,k);
n=m+k;
y=x;
graph
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
Code
n=-2:10;
x=[1,2,3,4,5,6,7,6,5,4,3,2,1];
subplot(2,2,1);
stem(n,x);
xlabel('discrete n');
ylabel('amplitude in discrete');
title('plot of x function');
x1=sigshift(2*x,n,5);
x2=sigshift(3*x,n,-4);
n1=3:15;
[191𝐴017]
n2=-6:6;
n3=-6:15;
x3= sigadd(x1,n1,x2,n2);
subplot(2,2,2);
stem(n3,x3);grid on;
xlabel('discrete n');
ylabel('amplitude in discrete');
title('plot of y function');
function sigadd.m
function [y,n]= sigadd(x1,n1,x2,n2);
m1=min(min(n1),min(n2));
m2=max(max(n1),max(n2));
n=m1:m2;
y1=[zeros(1,abs(min(n1)-m1)) x1 zeros(1,abs(max(n1)-m2))];
y2=[zeros(1,abs(min(n2)-m1)) x2 zeros(1,abs(max(n2)-m2))];
y=y1-y2;
graph
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
[191𝐴017]
Code
n=-4:8;
x=[1,2,3,4,5,6,7,6,5,4,3,2,1];
subplot(2,2,1);
stem(n,x);
xlabel('discrete n');
ylabel('amplitude in discrete');
title('plot of x function');
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
n1=-5:7;
n2=-2:10;
x1=sigshift(x,n,2);
x2=sigshift(x,n,-3);
x3=sigfold(x2,n1);
x4=x1.*x;
subplot(2,2,2);
stem(n2,x4);
xlabel('discrete n');
ylabel('amplitude in discrete');
title('plot of x4 function');
n4=-2:8;
x5=sigadd(x2,n1,x4,n2);
n3=-5:10;
subplot(2,2,3);
stem(n3,x5);
grid on;
xlabel('discrete n');
ylabel('amplitude in discrete');
title('plot of y function');
Function
function [y,n]= sigadd(x1,n1,x2,n2);
m1=min(min(n1),min(n2));
m2=max(max(n1),max(n2));
n=m1:m2;
y1=[zeros(1,abs(min(n1)-m1)) x1 zeros(1,abs(max(n1)-m2))];
y2=[zeros(1,abs(min(n2)-m1)) x2 zeros(1,abs(max(n2)-m2))];
y=y1+y2;
Graph
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
[191𝐴017]
Code
n=-10:10;
x=exp((-.1+j.*0.3).*n);
subplot(2,2,1);
stem(n,abs(x));
title('magnitude plot');
xlabel('discrete n');
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
ylabel('amplitude in discrete');
subplot(2,2,2);
stem(n,angle(x));
title('phase plot');
xlabel('discrete n');
ylabel('phase in y');
x2=sigfold(x,n);
[191𝐴017]
x3=0.5*(x+x2);
subplot(2,2,3);
stem(n,x3);
title('even plot');
xlabel('discrete n');
ylabel('amplitude in discrete');
x3=0.5*(x-x2);
subplot(2,2,4);
stem(n,x3);
title('odd plot');
xlabel('discrete n');
ylabel('amplitude in discrete');
Function
function [y,n]=sigfold(x,m);
n=-fliplr(m);
y=fliplr(x);
Graph
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
Code
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
t=-13:13;
x1=2*stepseq(-10,-13,13)-2*stepseq(5,-13,13);;
subplot(2,2,1);
plot(t,x1);
grid on;
xlabel('time t');
ylabel('amplitude ');
title('plot of x1 function');
x2=0.66*(t.*stepseq(-3,-13,13)+t.*stepseq(3,13,13)+3*stepseq(-3,-13,13)-3*stepseq(3,-13,13))1.33*t.*stepseq(0,-13,13);
subplot(2,2,2);
plot(t,x2);grid on;
xlabel('time t');
ylabel('amplitude ');
title('plot of x2 function');
subplot(2,2,3);
x3=sigfold(x1,t);
plot(t,x3);grid on;
xlabel('time t');
ylabel('amplitude ');
title('plot of x3 function');
[191𝐴017]
Function
function [y,n]=sigfold(x,m);
n=-fliplr(m);
y=fliplr(x);
Graph
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
191A017 JATIN KATIYAR
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Signal and systems
tyuiopasdfghjklzxcvbnmqwertyuiopas
Lab 5
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Jatin katiyar
191a017
JATIN KATIYAR [191𝐴017]
Code
clc;
clear all;
n1=input('Enter range of first Sequence :');
n2=input('Enter range of second Sequence :');
x1=input('Enter first Sequence :');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
x2=input('Enter second Sequence :');
n=(min(n1)+min(n2):max(n1)+max(n2));
subplot(3,1,1);
stem(n1,x1);
xlabel('n1');
ylabel('x(n)');
title('First sequence');
subplot(3,1,2);
stem(n2,x2);
[191𝐴017]
xlabel('n2');
ylabel('h(n)');
title('Second sequence');
p=length(x1);
for i=1:p
hm=[zeros(1,i-1) x2 zeros(1,p-i)];
H(i,:) = hm;
end
y=x1*H;
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
disp('Convolution Sum y(n) = ');y
subplot(3,1,3);
stem(n,y);
xlabel('n');
ylabel('y(n)');
title('Convolution Sum');
[191𝐴017]
ans
Enter first Sequence :[3,11,7,0,-1,4,2];
Enter second Sequence :[2,3,0,-5,2,1];
Convolution Sum y(n) =
y=
6 31 47
6 -51 -5 41 18 -22 -3
8
2
Graph
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
CODE
clc;
clear all;
n1=input('Enter range of first Sequence :');
n2=input('Enter range of second Sequence :');
x1=input('Enter first Sequence :');
x2=input('Enter second Sequence :');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
n=(min(n1)+min(n2):max(n1)+max(n2));
subplot(3,1,1);
stem(n1,x1);
xlabel('n1');
ylabel('x(n)');
title('First sequence');
subplot(3,1,2);
stem(n2,x2);
xlabel('n2');
ylabel('h(n)');
title('Second sequence');
[191𝐴017]
p=length(x1);
for i=1:p
hm=[zeros(1,i-1) x2 zeros(1,p-i)];
H(i,:) = hm;
end
y=x1*H;
disp('Convolution Sum y(n) = ');y
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
subplot(3,1,3);
stem(n,y);
xlabel('n');
ylabel('y(n)');
title('Convolution Sum');
[191𝐴017]
ANSWER
nter second Sequence :-5:50;
Convolution Sum y(n) =
y=
Columns 1 through 16
0
0
0
0
0 -5 -9 -12 -14 -15 -15 -14 -12 -9 -5
5
Columns 17 through 32
15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165
Columns 33 through 48
175 185 195 205 215 225 235 245 255 265 275 285 295 305 315 325
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
Columns 49 through 64
335 345 355 365 375 385 395 405 415 425 435 445 455 414 372 329
Columns 65 through 80
285 240 194 147 99 50
0
0
0
0
0
0
0
0
0
0
Columns 81 through 96
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Columns 97 through 111
0
0
0
0
0
0
>>
GRAPH
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
[191𝐴017]
CODE
n=-25:25;
x1=cos((pi*n)/4).*(stepseq(-5,-25,25)-stepseq(25,-25,25));
x2= power(0.9,-n).*(stepseq(0,-25,25)-stepseq(20,-25,25));
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
n2=-10:10;
w=stepseq(-10,-10,10);
x3=round(5*w);
% subplot(2,2,1);
% stem(n,x1);
% xlabel('n1');
% ylabel('x1(n)');
% title('plot of input x1(n)');
%
% subplot(2,2,2);
% stem(n,x2);
[191𝐴017]
% xlabel('n1');
% ylabel('x2(n)');
% title('plot of input x2(n)');
%
% subplot(2,2,3);
% stem(n2,x3);
% xlabel('n1');
% ylabel('x3(n)');
% title('plot of input x3(n)');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
[y1,m1]=conv_sum(x2,n,x1,n);
[y2,m2]=conv_sum(x3,n2,y1,m1);
subplot(2,2,1);
stem(m1,y1);
xlabel('m1');
ylabel('y1(n)');
title('plot of input y1(n)');
subplot(2,2,2);
stem(m2,y2);
[191𝐴017]
xlabel('m2');
ylabel('y2(n)');
title('plot of input y2(n)');
[y3,m3]=conv_sum(x3,n2,x1,n);
[y4,m4]=conv_sum(x2,n,y3,m3);
subplot(2,2,3);
stem(m4,y4);
xlabel('m4');
ylabel('y4(n)');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
title('plot of input y4(n)');
GRAPH
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
CODE
clc;
clear all;
a=[1];
b=[1 -1 0.9];
n=-10:120;
h=impz(a,b,n);
subplot(2,1,1);
stem(n,h);
xlabel('n');
ylabel('amplitude');
title('impluse response');
x=[zeros(1,10),ones(1,121)];
u=filter(a,b,x);
subplot(2,1,2)
stem(n,u);
xlabel('n');
ylabel('amplitude');
title('unitstep response');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
CODE
clc;
clear all;
n=-3:4;
x=[3 8 7 2 0 -3 4 5];
w=rand(1,length(n));
[x2,n2]=sigshift(x,n,2);
[y,m]=sigadd(x2,n2,w,n);
[x1,n1]=sigfold(x,n);
[y1,m1]=conv_sum(x,n,x1,n1);
[y2,m2]=conv_sum(y,m,x1,n1);
subplot(2,2,1);
stem(n,x);
JATIN KATIYAR [191𝐴017]
[191𝐴017]
JATIN KATIYAR [191𝐴017]
xlabel('n1');
ylabel('x(n)');
title('plot of input x(n)');
subplot(2,2,2);
stem(m,y);
xlabel('m');
ylabel('y(n)');
title('plot of input y(n)');
subplot(2,2,3);
stem(m1,y1);
xlabel('m1');
ylabel('rxx(n)');
title('autocorrelation');
subplot(2,2,4);
stem(m2,y2);
xlabel('n1');
ylabel('rxy(n)');
title('crosscorrelation');
JATIN KATIYAR [191𝐴017]
JATIN KATIYAR [191𝐴017]
GRAPH
JATIN KATIYAR [191𝐴017]
191A017
JATIN KATIYAR
SIGNALS AND SYSTEMS LAB NO.01
JATIN KATIYAR 191A017
Signals & Systems Lab: Experiment # 1
Exercise#1
(a) Generate a matrix of size 4x4 of normally distributed random numbers.
(b) Change the value of the 3rd column to [6 9 2 5].
(c) Delete the 2nd row.
[191𝐴017]
code
a_17=randn(4,4)
a_17(:,[3])=[6 9 2 5]
a_17(2,:)=[]
ans
a_17 =
0.5377
1.8339
-2.2588
0.8622
0.3188
-1.3077
-0.4336
0.3426
3.5784
2.7694
-1.3499
3.0349
0.7254
-0.0631
0.7147
-0.2050
0.3188
-1.3077
-0.4336
0.3426
6.0000
9.0000
2.0000
5.0000
0.7254
-0.0631
0.7147
-0.2050
a_17 =
0.5377
1.8339
-2.2588
0.8622
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
a_17 =
0.5377
-2.2588
0.8622
0.3188
-0.4336
0.3426
6.0000
2.0000
5.0000
0.7254
0.7147
-0.2050
Exercise#2
(a) Start with the 4-by-4 square, A.
(b) Then form B = [A A+32; A+48 A+16]
(c) What’s the size of B?
Code
a=[1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]
b=[ a, a+32 ;a+48, a+16]
s=size(b)
ans
a=
1
2
3
4
5
6
7
8
9 10 11 12
13 14 15 16
b=
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
1
2
3
4 33 34 35 36
5
6
7
8 37 38 39 40
9 10 11 12 41 42 43 44
13 14 15 16 45 46 47 48
49 50 51 52 17 18 19 20
53 54 55 56 21 22 23 24
57 58 59 60 25 26 27 28
61 62 63 64 29 30 31 32
s=
8
8
[191𝐴017]
Exercise#3
Define the following discrete time signal using concatenation
code
n1=0:9;
x1=0.8+n1*0;
n2=10:19;
x2=0+n2*0;
n3=20:30;
x3=n3.^0.2+n3*0;
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
n=[n1 n2 n3];
x=[x1 x2 x3];
stem(n,x)
ans
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
Code
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
a_17=[2 -2;-1 2]
b_17=[1 -1;0 2]
c_17=[1;-2]
d_17=a_17+b_17
%e_17=a_17+c_17 invalid
f_17=b_17+d_17
g_17=b_17*c_17
h_17=a_17*b_17
i_17=a_17/d_17
%j_17=(c_17*c_17)*a_17 invlid
%k_17=(c_17.*c_17)*a_17 invalid
Ans
a_17 =
2 -2
-1
2
b_17 =
1 -1
0
2
c_17 =
1
-2
JATIN KATIYAR 191A017
[191𝐴017]
JATIN KATIYAR 191A017
d_17 =
3 -3
-1
4
f_17 =
4 -4
-1
6
g_17 =
3
-4
h_17 =
2 -6
-1
5
i_17 =
0.6667
0
-0.2222 0.3333
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
Code
a_17=1:2:5
x=size(a_17)
b_17=[a_17' a_17' a_17']
y=size(b_17)
c_17=b_17(1:2:3,1:2:3)
z=size(c_17)
d_17=a_17+b_17(2,:)
t=size(d_17)
e_17=[zeros(1,3) ones(3,1)' 3:5]
r=size(e_17)
ans
a_17 =
[191𝐴017]
1
3
5
x=
1
3
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017
b_17 =
1
1
1
3
3
3
5
5
5
y=
3
3
c_17 =
1
5
5
2
2
z=
d_17 =
4
6
8
JATIN KATIYAR 191A017
1[191𝐴017]
JATIN KATIYAR 191A017
t=
1
3
e_17 =
0
0
1
9
0
1
1
1
r=
>>
JATIN KATIYAR 191A017
3
4
5
JATIN KATIYAR 191A017
JATIN KATIYAR 191A017