PROBLEM WITH THE PLOT OF FOURIER SERIES

Hii everyone I have a small problem with the series,

the plot i am doind is not right this should be a plot at a height of 2 and I dont know why this is not what i get

this is what i want to plot when N=100 :

and this is what i get

this is my code :

clc;clear;close all;
syms t k 
%D%
T=4; % Period Time
%D%
XT=[1,t,0]
ck=@(x,A,B)(1/T)*int((x*exp(2*pi*k*1i*t/-4)),t,[A,B])
ck1=ck(XT(1),0,1)
ck2=ck(XT(2),1,2)
ck3=ck(XT(3),2,4)
cktotal=ck1+ck2+ck3
%D.1%
NAGATIVESIDE5=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,-5,-1)
POSATIVESIDE5=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,+1,+5)
ALLBUTNOTZERO5=NAGATIVESIDE5+POSATIVESIDE5
%D.2%
NAGATIVESIDE10=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,-10,-1)
POSATIVESIDE10=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,1,10)
ALLBUTNOTZERO10=NAGATIVESIDE10+POSATIVESIDE10
%D.3%
NAGATIVESIDE100=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,-100,-1)
POSATIVESIDE100=symsum(cktotal*exp((2*pi*1i*k*t)/4),k,1,100)
ALLBUTNOTZERO100=NAGATIVESIDE100+POSATIVESIDE100
%plots%
fplot(ALLBUTNOTZERO5,[-10 10],"r")
ylabel("fourier approximation N=-5-->5")
xlabel("time")
grid on 
ylim([0 2])
fplot(ALLBUTNOTZERO10,[-10 10],"g")
ylabel("fourier approximation N=-10-->10")
xlabel("time")
grid on 
ylim([0 2])
fplot(ALLBUTNOTZERO100,[-10 10],"b")
ylabel("fourier approximation N=-100-->100")
xlabel("time")
grid on 
ylim([0 2])

Answer 1

[Yash]

Hi Daniel,

I understand that you are facing issues while calculating the Complex Fourier Series of the given piecewise function.

Upon reviewing your code, I have discovered that all the coefficients calculated by you are correct. However, you have not considered the coefficient for "k" equal to zero. You might have encountered a "Division by zero" error while substituting zero in the function for "ck". To overcome this issue, you can calculate the coefficient "c0" separately as follows:

c0 = (1/(2*L))*(int(XT(1),0,1)+int(XT(2),1,2)+ int(XT(3),2,4))

After calculating the coefficient "c0", you need to include it in your function calculation as shown below:

ALLBUTNOTZERO5=c0+NAGATIVESIDE5+POSATIVESIDE5;

By making these adjustments, the peak value should reach the desired value. You can refer to the obtained plot for N=100 below:

I hope this addresses your query.

Best Regards

Yash