Windowing in DSP

[from former notes]

Windowing is the process of taking small subset of large dataset for processing or analysis.

Naive method "rectangular window" will cause power leak - if the signal is a lowpass signal, windowing will introduce high frequency component. Re-distribution of power from target band to upper freq is power leakage.

Windowing multiply a signal x[n] or impulse response h[n] by a given finite sequence w[n]

x_w[n] = x[n] w[n], where w[n] = 0 when n < 0 or n >= N

2  principle applications for Windowing:

• In the analysis of signal x[n], we usually process finite-length segment x_w[n] obtained by windowing x[n].

• Windowing is also used for filter design: to design an FIR filter, one approach is to window the impulse response of the ideal filter, which usually has infinite duration.

Types:

• Hamming: w[n] = 0.54 - 0.46cos(2PI n/N),   0<n<N
• Hann:       w[n] = 0.5 -0.5 cos(2PI n/N)
• blackman: w[n] = 0.42 - 0.5 cos(2PI n/N) + 0.08 cos (4PI n/N)
• chebyshev w[n] =
• rectangular:w[n] = 1,   0<= n <=N