Figure 3.29 shows an overlay of DPSS and Kaiser windows
for some different
values. In all cases, the window length
was
. Note how the two windows become more similar as
increases. The Matlab for computing the windows is as follows:
w1 = dpss(M,alpha,1); % discrete prolate spheroidal seq. w2 = kaiser(M,alpha*pi); % corresponding kaiser window
The following Matlab comparison of the DPSS and Kaiser windows
illustrates the interpretation of
as the bin number of the
edge of the critically sampled window main lobe, i.e., when the DFT
length equals the window length:
format long; M=17; alpha=5; abs(fft([ dpss(M,alpha,1), kaiser(M,pi*alpha)/2])) ans = 2.82707022360190 2.50908747431366 2.00652719015325 1.92930705688346 0.68469697658600 0.85272343521683 0.09415916813555 0.19546670371747 0.00311639169878 0.01773139505899 0.00000050775691 0.00022611995322 0.00000003737279 0.00000123787805 0.00000000262633 0.00000066206722 0.00000007448708 0.00000034793207 0.00000007448708 0.00000034793207 0.00000000262633 0.00000066206722 0.00000003737279 0.00000123787805 0.00000050775691 0.00022611995322 0.00311639169878 0.01773139505899 0.09415916813555 0.19546670371747 0.68469697658600 0.85272343521683 2.00652719015325 1.92930705688346
Finally, Fig.3.30 shows a comparison of DPSS and Kaiser window transforms, where the DPSS window was computed using the simple method listed in §F.1.2. We see that the DPSS window has a slightly narrower main lobe and lower overall side-lobe levels, although its side lobes are higher far from the main lobe. Thus, the DPSS window has slightly better overall specifications, while Kaiser-window side lobes have a steeper roll off.