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Matlab for the DPSS Window

The function dpss in the Matlab Signal Processing Tool Box4.10 can be used to compute them as follows:

  w = dpss(M,alpha,1); % discrete prolate spheroidal sequence
where $ M$ is the desired window length, and $ \alpha\in[0,M/2)$ can be interpreted as half of the window's time-bandwidth product $ \Delta
t\cdot \Delta f$ in ``cycles''. Alternatively, $ \alpha $ can be interpreted as the highest bin number $ k$ inside the main lobe of the window transform $ W(\omega_k)=\hbox{\sc DFT}_M(w)$ , when the DFT length is equal to the window length $ M$ . (See the next section on the Kaiser window for more on this point.)

Some examples of DPSS windows and window transforms are given in Fig.3.29.

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
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Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University