Graphing complex fourier series

Hi MatLab Community, I hope you are well

I've been trying to plot the graph of a complex fourier series and I haven´t be able to do it

The original signal x(t) is an square with To = 1 and Wo = 2*pi,

x(t) = 1, -1/4<= t <= 1/4, -1 something else

I calculated the C_n coefficient and it is

C_n = (1/(pi*n))*sin((pi*n)/2)+(1/(1i*2*pi*n))*(exp(-1i*3*pi*n/2)-exp(-1i*pi*n/2))

But when I tried to plot it a warning "Warning: Imaginary parts of complex X and/or Y arguments ignored. " appears

If I expand x(t) by the trigonometric method I could plot the Fourier series succesfully

This is my code.

T = 1;

W = (2*pi)/T;

t = [-2*pi:0.0001:2*pi];

x_t = 0;

for n = -100:100

C_n = (1/(pi*n))*sin((pi*n)/2)+(1/(1i*2*pi*n))*(exp(-1i*3*pi*n/2)-exp(-1i*pi*n/2));

x_t = x_t + C_n*exp(1i*n*W*t);

end

plot(t,x_t)

I hope you could help me, thank you

Answer 1

[Priyanshu Mishra]

Hi Santiago,

You are getting this warning because you are attempting to plot a complex input with plot function. If you want to plot imaginary part, I would suggest you pass the imaginary part to the plot function. For reference you may use this code :

T = 1;

W = (2*pi)/T;

t = [-2*pi:0.0001:2*pi];

x_t = 0;

for n = -100:100

C_n = (1/(pi*n))*sin((pi*n)/2)+(1/(1i*2*pi*n))*(exp(-1i*3*pi*n/2)-exp(-1i*pi*n/2));

x_t = x_t + C_n*exp(1i*n*W*t);

end

plot(t,imag(x_t))