dpss

Signal Processing Toolbox

Discrete prolate spheroidal sequences (Slepian sequences).

[e,v] = dpss(n,nw)
[e,v] = dpss(n,nw,'calc')
[e,v] = dpss(n,nw,'spline')
[e,v] = dpss(n,nw,'spline',Ni)
[e,v] = dpss(n,nw,'linear')
[e,v] = dpss(n,nw,'linear',Ni)
[e,v] = dpss(n,nw,'trace')
[e,v] = dpss(n,nw,'int','trace')

Description

[e,v] = dpss(n,nw)

generates the first 2*nw discrete prolate spheroidal sequences (DPSS) of length n, in the columns of e, and their corresponding concentrations in vector v. They are generated in the DPSS MAT-file database dpss.mat.

The sequences are generated in the frequency band || (2W), where
W = nw/n is the half-bandwidth and is in radians.
e(:,1) is the length n signal most concentrated in the frequency band
|| (2W) radians, e(:,2) is the signal orthogonal to e(:,1) that is most concentrated in this band, e(:,3) is the signal orthogonal to both e(:,1) and e(:,2) that is most concentrated in this band, etc.
For multitaper spectral analysis, typical choices for nw are 2, 5/2, 3, 7/2, or 4.

If you specify only n and nw, DPSS follows these rules for selecting an efficient (although sometimes approximate) algorithm:

If n < 500, the sequences are calculated directly.
If n 500,
1. look for sequences in the DPSS MAT-file database dpss.mat;
2. if not found, linearly interpolate from sequences with the same nw and next largest n in the database;
3. if not found, use spline interpolation from length 64 sequences.

[e,v] = dpss(n,nw,'calc')

forces DPSS to calculate e and v directly. This can take a long time for large n and nw.

[e,v] = dpss(n,nw,'spline')

uses spline interpolation to compute e and v from the sequences in dpss.mat with length closest to n.

[e,v] = dpss(n,nw,'spline',Ni)

interpolates from existing length Ni sequences.

[e,v] = dpss(n,nw,'linear')

and

[e,v] = dpss(n,nw,'linear',Ni)

use linear interpolation, which is much faster but less accurate than spline interpolation. 'linear' requires Ni > n.

[e,v] = dpss(n,nw,'trace')

and

[e,v] = dpss(n,nw,'int','trace')

use a trailing 'trace' argument to find out which method DPSS uses, where 'int' is either 'spline' or 'linear'.

See Also


`dpssclear`	Remove discrete prolate spheroidal sequences from database.
`dpssdir`	Discrete prolate spheroidal sequences database directory.
`dpssload`	Load discrete prolate spheroidal sequences from database.
`dpsssave`	Save discrete prolate spheroidal sequences in database.
`pmtm`	Power spectrum estimate using the multitaper method (MTM).

References

[1] Percival, D.B., and A.T. Walden. Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge: Cambridge University Press, 1993.

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