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.