After sampling the signal, we limit the duration of the signal to the time interval T0=LT, where L is the number of samples and T is the sample interval. So, it limits our ability to distinguish two frequency components that are separated by less than 1/T0=1/LT in frequency. So, the finite observation interval for the signal places a limit on the frequency resolution.

When the number of samples L is small, the window spectrum masks the signal spectrum and, consequently, the DFT of the data reflects the spectral characteristics of the window function. So, this situation should be avoided.

According to the exponential properties of Fourier transform, we get

We know that, after passing the signal through anti-aliasing filter, the filtered signal is sampled at a rate of Fs≥ 2B=>B≤ Fs/2.Thus the maximum frequency of the sampled signal is Fs/2.

We note that the windowed spectrum \\(\\hat{X}\\)(w) is not localized to a single frequency, but instead it is spread out over the whole frequency range. Thus the power of the original signal sequence x(n) that was concentrated at a single frequency has been spread by the window into the entire frequency range. We say that the power has been leaked out into the entire frequency range and this phenomenon is called as “Leakage”.

In the magnitude response of the signal windowed using Hanning window, the width of the main lobe is more which is the disadvantage of this technique over rectangular windowing technique.

We know that the equation for the rectangular window w(n) is given as

The equation of the rectangular window w(n) is given as

The filtered signal is sampled at a rate of Fs≥ 2B, where B is the bandwidth of the filtered signal to prevent aliasing.

The Hanning window has less side lobes and the leakage is less in this windowing technique.