SS Lab Class No 09

%{
 SS Lab Class no 09
 Date: 20.11.2019
 Place: CL3
 Time: 10.30 AM -12.30 AM
 Minhaj Rahat Sir
%}
clc;
clear all;
close all;
syms t;
x = heaviside(t+6)-heaviside(t-6);
T =12;
w = 2*pi/T;
k = -100:100;
an =(1/T)*int(x*exp(-j*k*w*t),t,-6,6);
xn = sum(an.*exp(j*k*w*t));
figure
ezplot(xn,[0,10]);
%% Experiment 02
clc;
clear all;
close all;
syms t w
a = 0.5;
f = exp(-a*t) * heaviside(t);
an = fourier(f,w);
ww = -2*a:.1:2*a;
a = subs(an,w,ww);
subplot(2,1,1)
plot(ww,abs(a))
xlabel('Frequency');
ylabel('Amplitude');
subplot(2,1,2)
plot(ww,angle(a))
xlabel('Frequency');
ylabel('phase(radian)');
%% Fourier Representaion of Square Wave
syms t w
f = heaviside(t+6)-heaviside(t-6);
To = 6;
an = fourier(f,w);
ww = -3*pi/To:.001:3*pi/To;
a = subs(an,w,ww);
subplot(2,1,1)
plot(ww,abs(a))
xlabel('Frequency');
ylabel('Amplitude');
subplot(2,1,2)
plot(ww,angle(a))
xlabel('Frequency');
ylabel('phase(radian)');
%% Linearity of Fourier Transform
syms t
a1 =3; a2 =2; x1 = exp(-3*t); x2 = exp(-t);
x = a1*x1 +a2*x2;
left = fourier(x,w);
right = fourier(a1*x1,w) + fourier(a2*x2,w);

ww = -10:.01:10;
left = subs(left,w,ww);
right = subs(right,w,ww);
plot(ww,abs(left),'r',ww,abs(right),'*')