MATLAB: How can i perform a Fourier series on this function

fourier_seriesmat lab

clear all;

close all;

clc;

syms n t1 t2 T f0 t;%t2=T;

func=(f0/t2-t1)*(t-t1);

n=1:10;

syms t t1 T;%T=t2;

w = (2*pi)/T;

a0 = (2/T)*int(func,t,0,T);

an = (2/T)*int(func*cos(n*w*t),t,0, T);

bn = (2/T)*int(func*sin(n*w*t),t, 0,T);

f = a0/2 + dot(an,cos(n*w*t)) + dot (bn, sin(n*w*t));

ezplot(func);

hold on;

grid on;

plot(f);

Best Answer

Here is the full solution to your problem. Good luck.

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MATLAB: How to write a sigma calculation

In part two of the problem, you will have to use the definition of the DTFT to compute X(omega). The resultant function is just a periodic version of X(jw) from part one of the problem. See the following code below.

%%Part 1
clear variables
close all
N= 200;
T = 2;
t  = -2:4/(N-1):2;
x = rectpuls(t,T);
f= -2:4/(N-1):2;
X = T*sin(pi*f*T)./(pi*f*T);
figure
subplot(121)
plot(t,x,'linewidth',2,'color','b')
grid;
a = title('x(t)');
set(a,'fontsize',14);
a = ylabel('x');
set(a,'Fontsize',14);
a = xlabel('t');
set(a,'Fontsize',14);
subplot(122)
plot(f,abs(X)/(max(X)),'linewidth',2,'color','m')
a = title('|X(jw)|');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid
%%Part 2
M = 1000;
N = 7;
n = 0:N-1;
xn = ones(1,N);
w = 8*pi;
omega = -w:2*w/(M-1):w; 
Xn= exp(-1i.*omega.*(N-1)./2).*(sin(omega*N/2)./sin(omega/2)); %define DTFT function
Mag = abs(Xn)/max(Xn);   %compute magnitude
Phase = angle(Xn);       %compute phase
figure
subplot(3,1,1)
stem(n,xn,'linewidth',2,'color','b'); 
a = title('x(n)');
set(a,'fontsize',14);
a = ylabel('xn');
set(a,'Fontsize',14);
a = xlabel('n');
set(a,'Fontsize',14);
grid
subplot(3,1,2)
plot(omega/pi,real(Mag),'linewidth',2,'color','k'); 
a = title('|X(\omega)|');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid
subplot(3,1,3)
plot(omega./pi,Phase,'linewidth',2,'color','k'); 
a = title('<X(\omega)');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid

MATLAB: Can anyone explain how the phase angle should look like for a square pulse with pulse width 1 that has undergone FFT in matlab

The phase of a symmetric square pulse is uniformly zero, because the Fourier transform is purely real:

syms w t 
FTpulse = int(1*exp(1j*w*t), t, -0.5, 0.5)
FTpulse =
(2*sin(w/2))/w

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MATLAB: How to write a sigma calculation

MATLAB: Can anyone explain how the phase angle should look like for a square pulse with pulse width 1 that has undergone FFT in matlab

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