Frequency Response
Underlying the discrete sequence is this continuous-time function and its Fourier transform:
The maximum value of w(t) is w(0) = 1. The wn sequence defined above are the samples of:
- for all integer values of t,
and where rect is the rectangle function.
The smaller the value of |α|, the narrower the window becomes; α = 0 corresponds to a rectangular window. Conversely, for larger |α| the main lobe of increases in width, while the side lobes decrease in amplitude. Thus, this parameter controls the tradeoff between main-lobe width and side-lobe area, as is illustrated in the plot of the frequency spectra below. For large α, the shape of the Kaiser window (in both time and frequency domain) tends to a Gaussian curve. The Kaiser window is nearly optimal in the sense of its peak's concentration around ω = 0 (Oppenheim et al., 1999).
Read more about this topic: Kaiser Window
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