dpss.taper: Calculating Thomson's Spectral Multitapers by Inverse...

In bjw34032/waveslim: Basic Wavelet Routines for One-, Two-, and Three-Dimensional Signal Processing

Calculating Thomson's Spectral Multitapers by Inverse Iteration

Description

The following function links the subroutines in "bell-p-w.o" to an R function in order to compute discrete prolate spheroidal sequences (dpss).

Usage

dpss.taper(n, k, nw = 4, nmax = 2^(ceiling(log(n, 2))))

Arguments

n	length of data taper(s)
k	number of data tapers; 1, 2, 3, ... (do not use 0!)
nw	product of length and half-bandwidth parameter (w)
nmax	maximum possible taper length, necessary for FORTRAN code

Details

Spectral estimation using a set of orthogonal tapers is becoming widely used and appreciated in scientific research. It produces direct spectral estimates with more than 2 df at each Fourier frequency, resulting in spectral estimators with reduced variance. Computation of the orthogonal tapers from the basic defining equation is difficult, however, due to the instability of the calculations – the eigenproblem is very poorly conditioned. In this article the severe numerical instability problems are illustrated and then a technique for stable calculation of the tapers – namely, inverse iteration – is described. Each iteration involves the solution of a matrix equation. Because the matrix has Toeplitz form, the Levinson recursions are used to rapidly solve the matrix equation. FORTRAN code for this method is available through the Statlib archive. An alternative stable method is also briefly reviewed.

Value

v	matrix of data tapers (cols = tapers)
eigen	eigenvalue associated with each data taper
iter	total number of iterations performed
n	same as input
w	half-bandwidth parameter
ifault	0 indicates success, see documentation for "bell-p-w" for information on non-zero values

Author(s)

B. Whitcher

References

B. Bell, D. B. Percival, and A. T. Walden (1993) Calculating Thomson's spectral multitapers by inverse iteration, Journal of Computational and Graphical Statistics, 2, No. 1, 119-130.

Percival, D. B. and A. T. Walden (1993) Spectral Estimation for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge University Press.

See Also

sine.taper.

bjw34032/waveslim documentation built on Aug. 18, 2022, 2:36 p.m.