Discrete prolate spheroidal or Slepian sequence database
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, then the
function overwrites the old values and issues a warning.
Create Database of Slepian Sequences
Construct discrete prolate spheroidal sequences of length 512. Specify a time-half-bandwidth product of 2.5.
seq_length = 512; time_halfbandwidth = 2.5; [dps_seq,lambda] = dpss(seq_length,time_halfbandwidth);
Create a database using the output Slepian sequences and frequency-domain concentration ratios. The function saves the database,
dpss.mat, in the current working directory. The output variable,
status, is 0 if there is success.
status = dpsssave(time_halfbandwidth,dps_seq,lambda)
status = 0
time_halfbandwidth — Time-half-bandwidth product
Time-half-bandwidth product, specified as a positive scalar. This argument
determines the frequency concentrations of the Slepian sequences in
dps_seq — Slepian sequences
Slepian sequences, specified as a matrix. The number of rows in
dps_seq is equal to the length of the
lambda — Frequency concentration ratios
Frequency concentration ratios of Slepian sequences in
dps_seq, specified as a vector. The length of
lambda is equal to the number of columns in
Discrete Prolate Spheroidal Sequences
The discrete prolate spheroidal or Slepian sequences derive from the following time-frequency concentration problem. For all finite-energy sequences index limited to some set , which sequence maximizes the following ratio:
where Fs is the sample rate and . 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 . 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.
Time Half Bandwidth Product
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 hertz by defining the time half bandwidth product as NW/Fs, where Fs is the sample rate.
Introduced before R2006a