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Fourier Series analysis of Triangular waveform

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khatus:
Fourier Series of Triangular waveform




this is the solution of Fourier series of a triangular waveform from the book Circuits and Networks: Analysis and Synthesis by Shyammohan S. Palli.
In this problem they have take the time period of the triangular waveform from  -π to +π instead of 0 to 2π.

Now, from -π to 0 the equation of the waveform is as shown below


and from 0 to +π the equation of the waveform is


Which gives


My question is,

If i take the interval from 0 to 2π.then from 0 to +π the equation of the waveform will be



and from +π to +2π the equation of the waveform will be



But this gives



which did not match with previous.My question is why they took the interval from -π to +π instead of 0 to 2π.

 I post my calculation here



Andy Watson:
Check the limits on your last integration and note that the upper limit is \$2\pi\$ - when you run the figures this should translate to \$(2\pi)^2\$, you appear to have used \$2(\pi^2)\$.

khatus:
Thanks Andy Watson .silly mistake causes problem

rhb:
Because the discrete Fourier transform is periodic over the semi-closed interval from (-Pi,Pi]  by definition.

I  had a very miserable couple of weeks at work because I overlooked the semi-closed part.

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