plotting Fourier series periodic signal ?

i have this homewrok which asked me to plot a fourier series

the issues:

1. i don't know how to change it from unit step function
2. i don't know how to plot it to the 2nd period

Answer 1

[Chandra]

Hi,

For plotting x(t) use stem function

T1 = 2;
T0 = 8;
x1 = ones(1,2*T1);        % 1 i.e., 0<t<T1
x2 = -1*ones(1,T0/2-T1);  %-1 i.e., T1<t<T0/2
x = [x2 x1 x2];
%x = [x x x];
%t = linspace(-12,12,length(x));
t = linspace(-4,4,length(x));  %comment this line if 6 and 7 lines are uncommented
stem(t,x);
axis([-15 15,-2 2]);

for fourier series of x, refer to this link

[Faisal Al-Wazir]

Hello chandra,

i did your code and the answer didn't match my hand calculations

[Chandra]

Hi,

Try the updated code

[Faisal Al-Wazir]

thanks it worked

can you help me with the rest of the qustion ?

i tried doing a code but someone told me it's wrong

the code:

clc

clear all

syms n t

T = 2;

w = 2*pi/T;

% Exponential Fourier series

C(n) = (1/T)*(int(4*exp(-1i*w*n*t),t,0,1)+int(-4*exp(-1i*w*n*t),t,1,2));

C0 = limit(C(n),n,0); % C(0)

Harmonics = [C0 C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14) C(15) C(16) C(17) C(18) C(19) C(20) C(21) C(22) C(23) C(24) C(25) C(26) C(27) C(28) C(29) C(30) C(31) C(32)];

fprintf('First 13 Harmonics:\n')

disp(Harmonics)

% f(t) using Fourier Series representation

f(t) = symsum(C(n)*exp(1i*w*n*t),n,-100,-1)+C0+symsum(C(n)*exp(1i*w*n*t),n,1,100);

fplot(t,f(t))

xlabel('t')

ylabel('f(t)')

title('f(t) using Fourier Series Coefficients')

grid on

[Faisal Al-Wazir]

BTW chandra

your code is right but only for one cycle or period .

[Chandra]

uncomment line 6 and 7 and comment line 8 then 3 cycles will be observed

[Chandra]

Hi,

Use the code below for output values with different harmonics

clc
clear all
syms n t
T = 8;
w = 2*pi/T;
% Exponential Fourier series
C(n) = (1/T)*(int(1*exp(-1i*w*n*t),t,0,2)+int(-1*exp(-1i*w*n*t),t,2,6)+int(1*exp(-1i*w*n*t),t,6,8));
C0 = limit(C(n),n,0); % C(0)
Harmonics = [C0 C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12)  C(13) C(14) C(15)  C(16) C(17) C(18) C(19) C(20) C(21) C(22) C(23) C(24) C(25) C(26) C(27) C(28)  C(29) C(30) C(31)  C(32)];
fprintf('First 13 Harmonics:\n')
Harmonics = Harmonics*2; %an = cn *2
disp(Harmonics)

% f(t) using Fourier Series representation
L = 4; % change values accordingly to 8, 16 32 
f(t) = symsum(C(n)*exp(1i*w*n*t),n,-L,-1)+C0+symsum(C(n)*exp(1i*w*n*t),n,1,L);
fplot(t,f(t))
xlabel('t')
ylabel('f(t)')
title('f(t) using Fourier Series Coefficients')
grid on

Change the L value accordingly as 4 , 8 , 16 , 32 ,etc..

frequency of a16 is 16*(1/8) = 2KHz.

[Faisal Al-Wazir]

Thanks chandra