Periodic rectangular function
Periodic rectangular function
(OP)
Question...
Can anybody tell me what happens to this equation when:
1. tau->0
2. T->infinity
http://en.wikipedia.org/wiki/Pulse_wave
I'm talking about the Fourier Series... The answer is not zero I guess. But I don't know what it is...
Please help!
Can anybody tell me what happens to this equation when:
1. tau->0
2. T->infinity
http://en.wikipedia.org/wiki/Pulse_wave
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
Cheers
Greg Locock
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RE: Periodic rectangular function
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
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.