spec.mtm {multitaper}

Compute and plot multitaper spectrum estimates

Description

Computes and plots adaptive or nonadaptive multitaper spectrum estimates from contiguous time series objects.

Usage

spec.mtm(timeSeries, nw=4.0, k=7, nFFT="default", taper=c("dpss"),
         centre=c("Slepian"), dpssIN=NULL, returnZeroFreq=TRUE,
         Ftest=FALSE, jackknife=FALSE, jkCIProb=.95, adaptiveWeighting=TRUE,
         maxAdaptiveIterations=100, plot=TRUE, na.action=na.fail,
         returnInternals=FALSE, sineAdaptive=FALSE, sineSmoothFact=0.2,
         dtUnits=c("default"), deltat=NULL, ...) 

Arguments

timeSeries

A time series of equally spaced data, this can be created by the ts() function where deltat is specified.

nw

nw a positive double precision number, the time-bandwidth parameter.

k

k a positive integer, the number of tapers, often 2*nw.

nFFT

This function pads the data before computing the fft. nFFT indicates the total length of the data after padding.

taper

Choose between dpss-based multitaper (the default,'dpss') or sine taper method. In the case of the sine taper, parameter nw is useless, and both Ftest and jackknife are forced to FALSE. The sine taper also has two specific parameters below.

centre

The time series is centred using one of three methods: expansion onto discrete prolate spheroidal sequences ('Slepian'), arithmetic mean ('arithMean'), trimmed mean ('trimMean'), or not at all ('none').

dpssIN

Allows the user to enter a dpss object which has already been created. This can save computation time when Slepians with the same bandwidth parameter and same number of tapers are used repeatedly.

returnZeroFreq

Boolean variable indicating if the zeroth frequency (DC component) should be returned for all applicable arrays.

Ftest

Boolean variable indicating if the Ftest result should be computed and returned.

jackknife

Boolean variable indicating if jackknifed confidence intervals should be computed and returned.

jkCIProb

Decimal value indicating the jackknife probability for calculating jackknife confidence intervals. The default returns a 95% confidence interval.

adaptiveWeighting

Boolean flag for enabling/disabling adaptively weighted spectrum estimates. Defaults to TRUE. The FALSE case gives complex Fourier transforms equivalent to direct estimates with Slepian sequences as tapers.

maxAdaptiveIterations

Maximum number of iterations in the adaptive multitaper calculation. Generally convergence is quick, and should require less than 100 iterations.

plot

Boolean variable indicating if the spectrum should be plotted.

na.action

Action to take if NAs exist in the data, the default is to fail.

returnInternals

Return the weighted eigencoefficients, complex mean values, and so on. These are necessary for extensions to the multitaper, including magnitude-squared coherence (function mtm.coh in this package). Note: The internal ($mtm) variables eigenCoefs and eigenCoefWt correspond to the multitaper eigencoefficients. The eigencoefficients correspond to equation (3.4) and weights, eigenCoefWt, correspond to sqrt(|d_k(f)|^2) from equation (5.4) in Thomson's 1982 paper. This is because the square root values contained in eigenCoefWt are commonly used in additional calculations (example: eigenCoefWt * eigenCoefs). The values returned in mtm$cmv correspond to the the estimate of the coefficients hat(mu)(f) in equation (13.5) in Thomson (1982), or to the estimate of hat(C)_1 at frequency 1 in equation (499) form Percival and Walden (1993)

sineAdaptive

In the case of using the sine taper method, choose between non-adaptive and adaptive taper choice.

sineSmoothFact

The sine taper option has an inherent smoothing parameter that can be set between 0.01 and 0.5. Lower values indicate smaller amounts of smoothing.

dtUnits

Allows indication of the units of delta-t for accurate frequency axis labels.

deltat

Time step for observations. If not in seconds, dtUnits should be set to indicate the proper units for plot labels.

...

Additional parameters, such as xaxs="i" which are passed to the plotting function. Not all parameters are supported.

Details

The value log can be set to “yes” (default), “no”, or “dB” as in the function plot.spec.

References

Thomson, D.J (1982) Spectrum estimation and harmonic analysis. Proceedings of the IEEE Volume 70, Number 9, pp. 1055–1096.

Percival, D.B. and Walden, A.T. (1993) Spectral analysis for physical applications Cambridge University Press.

Riedel, K.S. and Sidorenko, A. (1995) Minimum bias multiple taper spectral estimation. IEEE Transactions on Signal Processing Volume 43, Number 1, pp. 188–195.

See Also

plot.mtm and plot.spec

Examples

## default behaviour, dpss tapers; deltat and dtUnits set to ensure axis accuracy
data(willamette)
spec.mtm(willamette, nw=4.0, k=8, deltat=1/12, dtUnits="year")
spec.mtm(willamette, nw=4.0, k=8, nFFT=2048, deltat=1/12, dtUnits="year")

## if you have a ts object, you can skip the deltat and dtUnits parameters
will.ts <- ts(data=willamette, start=1950.75, freq=12)
spec.mtm(will.ts, nw=4.0, k=8)

## using Sine Tapers
spec.mtm(will.ts, k=10, taper="sine", sineAdaptive=FALSE)
spec.mtm(will.ts, k=10, taper="sine", sineAdaptive=TRUE, 
         maxAdaptiveIterations=100, sineSmoothFact=0.05)