I want to Fourier transform the 'y' function using Euler's formulas.

'y' is

x = [-pi:pi/10:pi];

sum=0;

y1=0;

for k=1:100

y1=(((cos(k*pi)-1).*cos(k*x))./(-pi*(k^2)));

sum=sum +y1;

end

y=sum+pi/2;

figure(1)

plot(x,y)

axis([-4 4 0.5 2.7])

I want to Fourier transform the 'y' function using Euler's formulas.

One cycle is 2pi. I'm not sure how to express this in Matlab. I need help.

Answer 1

[Mathieu NOE]

here you are my friend :

clc
x = [-pi:pi/10:pi];
sum=0;
y1=0;
for k=1:100
    y1=(((cos(k*pi)-1).*cos(k*x))./(-pi*(k^2)));
    sum=sum +y1;
end
y=sum+pi/2;

% fourier series 
a0 = trapz(x,y)/(2*pi);
m = 8;
for n = 1:m
    a(n) = trapz(x,y.*cos(n*x))/pi;
    b(n) = trapz(x,y.*sin(n*x))/pi;
end

% let's prove the fourier sum approximate y
yf = a0;
for n = 1:m
    yf = yf + a(n)*cos(n*x) + b(n)*sin(n*x);
end

figure(1)
plot(x,y,'b',x,yf,'*--r')
axis([-4 4 0.5 2.7])

[Dyuman Joshi]

@Mathieu NOE - A request from me, would you please shift your answer to this thread? https://in.mathworks.com/matlabcentral/answers/2054864-incorrect-number-or-types-of-inputs-or-outputs-for-function-int

This one is duplicate of the question I linked. And it would be better if all discussion was on a single thread.