Discrete prolate spheroidal (Slepian) sequences

`dps_seq = dpss(seq_length,time_halfbandwidth)`

[dps_seq,lambda] = dpss(seq_length,time_halfbandwidth)

[...] = dpss(seq_length,time_halfbandwidth,num_seq)

[...] = dpss(seq_length,time_halfbandwidth,'interp_method')

[...] = dpss(...,Ni)

[...] = dpss(...,'trace')

`dps_seq = dpss(seq_length,time_halfbandwidth)`

returns
the first `round(2*time_halfbandwidth)`

discrete
prolate spheroidal (DPSS), or Slepian sequences of length `seq_length`

. `dps_seq`

is
a matrix with `seq_length`

rows and `round(2*time_halfbandwidth)`

columns. `time_halfbandwidth`

must
be strictly less than `seq_length/2`

.

`[dps_seq,lambda] = dpss(seq_length,time_halfbandwidth)`

returns
the frequency-domain energy concentration ratios of the column vectors
in `dps_seq`

. The ratios represent the amount of
energy in the passband [*–W*,*W*]
to the total energy from [*–F _{s}*/2,

`lambda`

is a column vector equal in length
to the number of Slepian sequences.`[...] = dpss(seq_length,time_halfbandwidth,num_seq)`

returns
the first `num_seq`

Slepian sequences with time half
bandwidth product `time_halfbandwidth`

ordered by
their energy concentration ratios. If `num_seq`

is
a two-element vector, the returned Slepian sequences range from `num_seq(1)`

to `num_seq(2)`

.

`[...] = dpss(seq_length,time_halfbandwidth,'interp_method')`

uses
interpolation to compute the DPSSs from a user-created database of
DPSSs. Create the database of DPSSs with `dpsssave`

and
ensure that the resulting file, `dpss.mat`

, is in
the MATLAB^{®} search path. Valid options for `'interp_method'`

are `'spline'`

and `'linear'`

.
The interpolation method uses the Slepian sequences in the database
with time half bandwidth product `time_halfbandwidth`

and
length closest to `seq_length`

.

`[...] = dpss(...,Ni)`

interpolates from
DPSSs of length `Ni`

in the database dpss.mat.

`[...] = dpss(...,'trace')`

prints the method
used to compute the DPSSs in the command window. Possible methods
include: direct, spline interpolation, and linear interpolation.

Percival, D. B., and A. T. Walden. *Spectral Analysis
for Physical Applications.* Cambridge, UK: Cambridge University
Press, 1993.

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