dpsssave(time_halfbandwith,dps_seq,lambda) status = dpsssave(time_halfbandwith,dps_seq,lambda)

Description

dpsssave(time_halfbandwith,dps_seq,lambda) creates
a database of discrete prolate spheroidal (DPSS) or Slepian sequences
and saves the results in dpss.mat. The time half
bandwidth producttime_halfbandwith is a real-valued
scalar determining the frequency concentration of the Slepian sequences
in dps_seq. dps_seq is a NxK matrix
of Slepian sequences where N is the length of the
sequences. lambda is a 1xK vector
containing the frequency concentration ratios of the Slepian sequences
in dps_seq.

If the database dpss.mat exists, subsequent
calls to dpsssave append the Slepian sequences
to the existing file. If the sequences are already in the existing
file, dpsssave overwrites the old values and issues
a warning.

status = dpsssave(time_halfbandwith,dps_seq,lambda) returns
a 0 if the database operation was successful or a 1 if unsuccessful.

Construct the first four discrete prolate spheroidal sequences of length 512. Specify a time half bandwidth product of 2.5. Use them to create a database of Slepian sequences, dpss.mat, in the current working directory. The output variable, status, is 0 if there is success.

The discrete prolate spheroidal or Slepian sequences derive
from the following time-frequency concentration problem. For all finite-energy
sequences $$x[n]$$ index limited to some set $$[{N}_{1},{N}_{1}+{N}_{2}]$$, which sequence maximizes the
following ratio:

where F_{s} is
the sampling frequency and $$\left|W\right|<Fs/2$$.
Accordingly, this ratio determines which index-limited sequence has
the largest proportion of its energy in the band [–W,W].
For index-limited sequences, the ratio must satisfy the inequality $$0<\lambda <1$$. The sequence maximizing the
ratio is the first discrete prolate spheroidal or Slepian sequence.
The second Slepian sequence maximizes the ratio and is orthogonal
to the first Slepian sequence. The third Slepian sequence maximizes
the ratio of integrals and is orthogonal to both the first and second
Slepian sequences. Continuing in this way, the Slepian sequences form
an orthogonal set of bandlimited sequences.

The time half bandwidth product is NW where N is
the length of the sequence and [–W,W]
is the effective bandwidth of the sequence. In constructing Slepian
sequences, you choose the desired sequence length and bandwidth 2W.
Both the sequence length and bandwidth affect how many Slepian sequences
have concentration ratios near one. As a rule, there are 2NW – 1 Slepian sequences with energy
concentration ratios approximately equal to one. Beyond 2NW – 1 Slepian sequences, the concentration
ratios begin to approach zero. Common choices for the time half bandwidth
product are: 2.5, 3, 3.5, and 4.

You can specify the bandwidth of the Slepian sequences in Hz
by defining the time half bandwidth product as NW/F_{s},
where F_{s} is the sampling
frequency.

References

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