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Graphing complex fourier series

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Santiago Restrepo García
Santiago Restrepo García on 15 May 2020
Answered: Priyanshu Mishra on 18 May 2020
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

Answers (1)

Priyanshu Mishra
Priyanshu Mishra on 18 May 2020
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))

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