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    <p>I can shed some light to the reason why "windowing" is applied before FFT is applied.</p> <p>As already pointed out the FFT assumes that we have a infinite signal. When we take a sample over a finite time T this is mathematically the equivalent of multiplying the signal with a rectangular function.</p> <p>Multiplying in the time domain becomes convolution in the frequency domain. The frequency response of a rectangle is the sync function i.e. sin(x)/x. The x in the numerator is the kicker, because it dies down O(1/N).</p> <p>If you have frequency components which are exactly multiples of 1/T this does not matter as the sync function is zero in all points except that frequency where it is 1.</p> <p>However if you have a sine which fall between 2 points you will see the sync function sampled on the frequency point. It lloks like a magnified version of the sync function and the 'ghost' signals caused by the convolution die down with 1/N or 6dB/octave. If you have a signal 60db above the noise floor, you will not see the noise for 1000 frequencies left and right from your main signal, it will be swamped by the "skirts" of the sync function.</p> <p>If you use a different time window you get a different frequency response, a cosine for example dies down with 1/x^2, there are specialized windows for different measurements. The Hanning window is often used as a general purpose window.</p> <p>The point is that the rectangular window used when not applying any "windowing function" creates far worse artefacts than a well chosen window. i.e by "distorting" the time samples we get a much better picture in the frequency domain which closer resembles "reality", or rather the "reality" we expect and want to see. </p>
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    1. POWhy do the convolution results have different lengths when performed in time domain vs in frequency domain?
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    1. USPeter Tillemans
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      1. VTUpMod
    1. CODo you mean *sinc* function and *Hamming* or *Hann* window?
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      1. USfinnw
 

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