SLEPTAP Calculate Slepian tapers. [PSI,LAMBDA]=SLEPTAP(M,P,K) calculates the K lowest-order Slepian tapers PSI of length M and time-bandwidth product P, together with their eigenvalues LAMBDA. PSI is M x K and LAMBDA is K x 1. K is optional and defaults to 2P-1. P is optional and defaults to 4. For M<=512, SLEPTAP uses the tridiagonal method described in Percival and Walden (1993). For M>512, it first computes tapers for M=512 and then spline-interpolates. (Tests show spline interpolation is far superior to linear interpolation for this problem.) The tapers are normalized to have unit energy. _____________________________________________________________________ Computing multiple taper lengths simultaneously M may also be an array of lengths. In this case PSI is a cell array of matrices, with PSI{1} being M(1) x K, PSI{2} being M(2) x K, etc., while LAMBDA is again K x 1. By default, SLEPTAP will down-interpolate the M=512 tapers to all shorter lengths, an approximation that is very good for data lengths greater than say M=64, and resulting in a vast computational savings. Because short data segments are difficult to extract reliable spectral information from anyway, this should be sufficient for most purposes. Alternatively, SLEPTAP(...,'exact') will directly compute solutions of PSI and LAMBDA for entries m for which M(m)<=512. In this case, LAMBDA will be a K x M matrix. This algorithm, like the default behavior, will spline-interpolate PSI from the M=512 solution to larger M values. SLEPTAP(...,'exact','parallel') will parallelize this computation using a PARFOR loop. This requires Matlab's Parallel Computing Toolbox. _____________________________________________________________________ See also MSPEC, MSVD, TWOSPECPLOT. 'sleptap --t' runs some tests. Usage: [psi,lambda]=sleptap(n); [psi,lambda]=sleptap(n,p,k); _________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2000--2021 J.M. Lilly --- type 'help jlab_license' for details