window function

Windowing of a simple waveform, like causes its Fourier transform to have non-zero values (commonly called spectral leakage) at frequencies other than ω. It tends to be worst (highest) near ω and least at frequencies farthest from ω.
If there are two sinusoids, with different frequencies, leakage can interfere with the ability to distinguish them spectrally. If their frequencies are dissimilar, then the leakage interferes when one sinusoid is much smaller in amplitude than the other. That is, its spectral component can be hidden by the leakage from the larger component. But when the frequencies are near each other, the leakage can be sufficient to interfere even when the sinusoids are equal strength; that is, they become unresolvable.


The rectangular window has excellent resolution characteristics for signals of comparable strength, but it is a poor choice for signals of disparate amplitudes. This characteristic is sometimes described as low-dynamic-range.

@rohit..we need the window function when we need to truncate a signal to be transmitted.Like a signal has the frequency range from 0 till infinity,but practical applications don't require infinite rnge frequencies.Suppose we need frequencies from 0 till 1MHz.I this case we use the simplest window function,a rctangular window.The rectangular window functin is like this

W={1; 0<f<=1MHz
{0; elsewhere

Thus,when the given infinite range signal is multiplied by this,the magnitude of the signal stays the same as its multiplied by only 1,whereas the range gets truncated as aftr 1MHZ the signal is multiplied by 0.

Final output={ signal; 0<f<=1 Mhz
{0,elsewhere

Thus,windowing is the most simple and powerful tool for signal processing.