Quote:
Originally Posted by

**Joe Bloggs**
It's not a matter of the FFT not 'liking' the discontinuity--it's just that a single cycle of a sine wave with silence before and after is a very different thing from a continuous sine tone and the difference in the FFT plot reflects that. But then you don't need me to tell you that lol

Case 1) Tone corresponds to an FFT bin and window is achieved by zero padding in the time domain:

If one applies a rectangular window to a tone in the time domain (meaning the tone abruptly starts and stops) then that corresponds, in the frequency domain, to convolving the FFT of a rectangular window (a sinc function) with the tone (a delta/single spike if the tone corresponds to an FFT bin.) Since the tone in this case is a delta, the result in the frequency domain is a **sinc function whose peak occurs at the tone frequency**. The lobe's width of the sinc is proportional to the size of the window. The larger the window (the more tone cycles in the time domain), the narrower the sinc...

Case 2) Tone does not correspond to an FFT bin:

One will get **side lobes** (instead of an delta in the frequency domain) when calculating the FFT of a tone, if the tone does not correspond to any of the FFT bin frequencies. Worst case scenario is if the tone frequency is half way between bins...

Hope this helps.

Edited by ultrabike - 10/14/12 at 9:43pm