[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.
- 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