mtm - Compute a spectrum by multitaper method.

SYNOPSIS

mtm [infile] -b bandwidth -f nfreq -s sig -w nwindows -v

DESCRIPTION

Mtm reads a data series from infile and calculates a power spectrum using the Multitaper Method (MTM). The method was developed by Thomson (1982); see also Yiou et al. (1994). It reduces power leakage and estimates uncertainties through simultaneous application of multiple, optimal windowing functions called Discrete Prolate Spheroidal Sequences (DPSS's). Mtm models the time series as a sum of sinusoids and calculates the corresponding amplitudes by a least-squares procedure. It also performs an F-test to identify weak spectral peaks and reject high-amplitude noise.

infile contains one column of (y) or two columns containing (x,y), separated by white space. If only one column is available, mtm assumes that delta_x is equal to 1. Comments are allowed at the beginning of the file. Comment lines start with 'c', '#', or '%'. If infile is not provided, mtm reads from the standard input.

A file called mtm.out is produced, containing three columns. Column One contains the frequencies, ranging from zero to the Nyquist frequency, in units which are the inverse of those in infile. Column Two contains the amplitudes of the spectrum. Column Three contains the results of the significance test for each frequency, in the range 0 to 1.

Another file, called mtm.sig, is also produced. It contains only those peaks deemed statistically signficant.

OPTIONS

-w
The number of window functions (i.e. DPSS's) to use for MTM. The recommended range is 1 to 20.
-b
Bandwidth for MTM as a multiple of the Nyquist frequency (1/(2*delta_x)) times the number of observations in the series. Thus a bandwidth of (5/N*delta_x) is entered as "-b 10". It is usually set to the number of windows plus or minus one.
-f
Set the number of frequencies to write when estimating the spectrum.
-s
Set the significance level in the interval [0,1]. Only peaks with an F-test greater than sig will be written to mtm.sig [default .9].
-v
Verbose mode. Mtm prints messages. (not implemented).

SEE ALSO

spectra(1)

REFERENCES

Thomson, D.J., 1982: Spectrum estimation and harmonic analysis, Proc. IEEE, 70, 1055-1096.

Yiou, P., M. Ghil, J. Jouzel, D. Paillard, and R. Vautard, 1994: Nonlinear variability of the climatic system, from singular and power spectra of Late Quaternary records, Clim. Dyn., 9, 371-389.

MTM 1 "10 May 1994"