Matlab for the DPSS Window

function [w,A,V] = dpssw(M,Wc);
% DPSSW - Digital Prolate Spheroidal Sequence window 
%         (Slepian window) of length M, having 
%         cut-off frequency Wc in (0,pi).
k = (1:M-1);
s = sin(Wc*k)./ k;
c0 = [Wc,s];
A = toeplitz(c0);   % c0=1st col of symm. Toeplitz mtx
[V,evals] = eig(A); % Only need principal eigenvector
[emax,imax] = max(abs(diag(evals)));
w = V(:,imax);
w = w / max(w);

Kaiser and DPSS Window Transforms Compared

• Kaiser $\approx$ DPSS
• DPSS window has a slightly narrower main lobe
• DPSS window has lower overall side-lobe levels
• Kaiser window side lobes roll off faster
• Otherwise they are very similar