Leakage in FFT Spectrum

When use FFT to compute the spectrum of a signal, we can only use a finitelength of signal, such as 512,1024 or 2048. This is equal to use a finint signal to multiple the analyze signal:
.
. xs(t)=x(t).u(t)
. Xs(f)=X(f)*U(f)
.
If x(t) is a sine signal and u(t) is a rectangle window signal, then we have:

The line spectrum of x(t) is leakeage to a continue spectrum of xs(t).

The applet below generate a sine signal, and cut it by a cut off function, then a zoom spectrum is used to showed the leakage of signal cut off. Several commonly used cut off function(windown function), rectangle window, hanning window, hamming window and blackman window, are listed.
Java Learning Program

Leakage of Signal Cutoff

Usage:
Select different window functions to cutoff the signal and to view their leakages in frequency.

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