Plotting the Fourier series for the function f=pi+x

I was trying to plot the Fourier series representation of the graph of (which should be a straight line).

And the Fourier series representation is given as:

This is the code that I'm using: ()

x=-pi:0.01:pi;
y=x+pi
Fr=0;
for i=1:100
an=((-1)*(i+1)*sin(i*x))/i;
Fr=Fr+2*an;
end
Fr=Fr+pi;
 plot(x,Fr)

But I'm getting a graph no where close to a straight line.

A help would be highly appreciated

[Walter Roberson]

The original is a straight line. The fourier transform of it is a delta function

https://dsp.stackexchange.com/questions/36552/fourier-transform-of-a-tilted-line-function

[Charith Silva]

Ah I see.

I misunerstood that both should have the same format.

Thanks for clarifying

Answer 1

[Star Strider]

You forgot to raise (-1) to a power. (You multiplied it instead.)

Try this:

an=((-1).^(i+1)*sin(i*x))/i;

Also, more terms produces a smoother plot.

To check the result, I did it without a loop:

n = 1:1E+3;
F = pi + 2*sum(sin(n(:)*x).*(-1).^(n(:)+1)./n(:));

figure
plot(x, F)

producing essentially the same plot.

[Charith Silva]

Thank you!!

[Star Strider]

As always, my pleasure!