dpsssave
Discrete prolate spheroidal or Slepian sequence database
Description
dpsssave(
creates a database of discrete prolate spheroidal (DPSS) or Slepian sequences and
saves the results in timeHalfBW
,dpsSeq
,lambda
)dpss.mat
.
Note
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.
saveFailureStatus = dpsssave(
returns a 0 if the database saving operation was successful or a 1 if
unsuccessful.timeHalfBW
,dpsSeq
,lambda
)
Examples
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 the function saves the database successfully.
status = dpsssave(time_halfbandwidth,dps_seq,lambda)
status = 0
Input Arguments
timeHalfBW
— Time-half-bandwidth product
positive scalar
Time-half-bandwidth product, specified as a positive scalar. This argument
determines the frequency concentrations of the Slepian sequences in
dpsSeq
.
Data Types: single
| double
dpsSeq
— Slepian sequences
matrix
Slepian sequences, specified as a matrix. The number of rows in
dpsSeq
is equal to the length of the
sequences.
Data Types: single
| double
lambda
— Frequency concentration ratios
vector
Frequency concentration ratios of Slepian sequences in
dpsSeq
, specified as a vector. The length of
lambda
is equal to the number of columns in
dpsSeq
.
Data Types: single
| double
More About
Structure of DPSS MAT- file Database
The dpsssave
function creates and stores a file named
dpss.mat
with the DPSS (Slepian sequences) that you generate with the
dpss
function.
The dpsssave
function assigns a location key (1
,
2
, …, n
) and a name (E1
,
V1
, E2
, V2
, ...,
En
, Vn
) for each Slepian sequence that it
generates and stores it in the dpss.mat
file, from the first to the
nth sequence.
A dpss.mat
file with n sequences presents the
following structure:
E1
,E2
, …,En
— Slepian sequences.V1
,V2
, …,Vn
— Frequency-domain energy concentration ratios.index
— Database index, astruct
array with information of the list of sequence lengths, time-half bandwidth products and locations of the Slepian sequences stored in the DPSS MAT-file database. This structure array comprises of the following fields:N
— Vector of sequence lengths. Thedpsssave
function assigns a single entry inN
for each different value of sequence length.Wlist
— Structure array of time-half bandwidth productsNW
and sequence location numberskey
. Thedpsssave
function assigns a sequence locationkey
to each Slepian sequence each time you call it.
next_key
— Next-sequence identification key, defined asnext_key=n+1
wheren
is the number of Slepian sequences stored in the DPSS MAT-file database.
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 this 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.
Version History
Introduced before R2006a
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