Kaiser and DPSS Windows Compared

Figure 3.23 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 sequence
  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.3.24 shows a comparison of DPSS and Kaiser window transforms, where the DPSS window was computed using the simple method listed in §G.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.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.