DFT, Sinc Function.

Cuthbert Nyack
Applet shows the DFT/DTFT of a sinc function f(t) = sinc(w1t). Since the spectrum of a rectangular wave is a sinc then the spectrum of the sinc should be a rectangular 'wave' with the unavoidable 'Gibbs' phenomenon.
eg parameters (3.4, NA, 0.0, 12.0, 27, 152, 100, NA, 15.0, 1.6)
This is the case of 4 samples per period of the sinc and the spectrum is a 'square wave'.
eg parameters (3.4, NA, 0.92, 12.0, 50, 46, 100, NA, 15.0, 2.8)
In this case the main lobe is not sampled and the spectrum approaches that of a damped sine at frequency w1.
eg parameters (3.4, NA, 0.0, 0.93, 20, 9, 40, NA, 2.0, 0.2)
Only the main lobe is sampled. The spectrum is a 'rectangular' wave with a very narrow +ve part.

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COPYRIGHT 2007 Cuthbert Nyack.