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No, Todd, the "period" that the sum repeats at can be "infinity".


Look at the derivation of a rectangular time-domain waveform. Make it easy, f(t), t <-1/2 =0, f(t), t> =-1/2, t <= 1/2 =1, f(t), 1> 1/2 =0;

Go ahead, follow the derivations on the net. Figure out the Fourier transform. NOT the DFT, the Fourier integral.

***poof*** there you have it. The frequency components are a sync function that goes to infinite frequency (this is not surprising since we picked out a function that has infinite slope at the first derivitive, that's also why the general rolloff of the function is 1/f).

Try it for a Gaussian of sigma = 1.

It is exactly, precisely, and provably the case that you can make ANY real signal out of the sum or integral of sine waves.

One can treat a DFT in two fashions, either as part of a periodic waveform, or as a rectangular-windowed signal with zero energy outside. The only difference is that the periodic interpretation means you have a Fourier SERIES, and the windowed signal has a continuous (in frequency) spectrum.

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