The peak side lobe in the case of Hanning window has a value of -32dB.

The frequency response shown in the figure is the frequency response of a low pass filter designed using a Blackman window of length M=61.

The transition width of the main lobe in the case of Blackman window is equal to 12Ï€/M where M is the length of the window.

The frequency response shown in the figure is the frequency response of a low pass filter designed using a Kaiser window of length M=61 and α=4.

Since the width of the main lobe is inversely proportional to the value of M, if the value of M increases then the main lobe becomes narrower.

The frequency of oscillations in the pass band of a low pass filter increases with an increase in the value of M, but they do not diminish in amplitude.

The larger side lobes of W(ω) results in the undesirable ringing effects in the FIR filter frequency response H(ω), and also in relatively large side lobes in H(ω).

The Hanning window has a time domain sequence as

The multiplication of hd(n) with a rectangular window is identical to truncating the Fourier series representation of the desired filter characteristic Hd(ω). The truncation of Fourier series is known to introduce ripples in the frequency response characteristic H(ω) due to the non-uniform convergence of the Fourier series at a discontinuity. The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.

The peak side lobe in the case of rectangular window has a value of -13dB.