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Periodic rectangular function

Periodic rectangular function

Periodic rectangular function


Can anybody tell me what happens to this equation when:

1. tau->0
2. T->infinity


I'm talking about the Fourier Series... The answer is not zero I guess. But I don't know what it is...

Please help!

RE: Periodic rectangular function

Thank you very much! BUT!!!

I wasn't saying tau~0 and T-> infinity at the same time :(

Plus I'm not talking about the FFT but the Fourier Series!

RE: Periodic rectangular function

What prompts you to ask? Is there an application or are you just curious? You have to admit, it looks a bit like homework...

To understand what happens in (1) and (2) (which are equivalent after timescaling), consider the parts of the FS equation:

1) the DC component, tau/T, goes to zero because the average content of the signal gets small as the pulse width gets small.

2) the cosine amplitudes, (2/n*pi)*sin(pi*n*tau/T), flatten out and get smaller. Plot the amplitude, replacing n with x and varying tau to see this happening - the graph will be continuous but the FS amplitudes are at periodic points on this line. As Greg indicates, the spectral components are "smearing" out to a flat line.

3) the cosines, cos(2*pi*n*t/T), are simply shifted to lower frequencies the bigger T is.


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