mtmPL: Multitaper Method Spectral Analysis with Power Law (1/f) fit

In astrochron: A Computational Tool for Astrochronology

Multitaper Method Spectral Analysis with Power Law (1/f) fit

Description

Multitaper Method (MTM) Spectral Analysis with Power Law (1/f) fit

Usage

mtmPL(dat,tbw=3,ntap=NULL,padfac=5,demean=T,detrend=F,siglevel=0.9,flow=NULL,fhigh=NULL,
    output=0,CLpwr=T,xmin=0,xmax=Nyq,pl=1,sigID=F,genplot=T,verbose=T)

Arguments

dat	Stratigraphic series for MTM spectral analysis. First column should be location (e.g., depth), second column should be data value.
tbw	MTM time-bandwidth product.
ntap	Number of DPSS tapers to use. By default, this is set to (2*tbw)-1.
padfac	Pad with zeros to (padfac*npts) points, where npts is the original number of data points.
demean	Remove mean from data series? (T or F)
detrend	Remove linear trend from data series? (T or F)
siglevel	Significance level for peak identification.
flow	Lowest frequency to include in 1/f fit
fhigh	Highest frequency to include in 1/f fit
output	What should be returned as a data frame? (0=nothing; 1=spectrum + CLs + power law fit; 2=sig peak freqs; 3=sig peak freqs + prob; 4=all)
CLpwr	Plot power law noise confidence levels on power spectrum (in addition to the power law fit)? (T or F)
xmin	Smallest frequency for plotting.
xmax	Largest frequency for plotting.
pl	Power spectrum plotting: (1) linear frequency-log spectral power, (2) linear frequency-linear spectral power (3) log frequency-log spectral power, (4) log frequency-linear spectral power
sigID	Identify signficant frequencies on power and probabilty plots? (T or F)
genplot	Generate summary plots? (T or F)
verbose	Verbose output? (T or F)

Details

Candidiate astronomical cycles are identified via isolation of those frequencies that achieve the required (e.g., 90 percent) power law confidence level and MTM harmonic F-test confidence level. Allowance is made for the smoothing inherent in the MTM power spectral estimate as compared to the MTM harmonic spectrum. That is, an F-test peak is reported if it achieves the required MTM harmonic confidence level, while also achieving the required power law confidence level within +/- half the power spectrum bandwidth resolution. One additional criterion is included to further reduce the false positive rate, a requirement that significant F-tests must occur on a local power spectrum high, which is parameterized as occurring above the local red noise background estimate. See Meyers (2012) for futher information.

The power spectrum normalization approach applied here divides the Fourier coefficients by the number of points (npts) in the stratigraphic series, which is equivalent to dividing the power by (npts*npts). The (npts*npts) normalization has the convenient property whereby – for an unpadded series – the sum of the power in the positive frequencies is equivalent to half of variance; the other half of the variance is in the negative frequencies.

Note that the 'spec.mtm' function in package 'multitaper' (Rahim et al., 2014) is used for MTM spectrum estimation.

References

S.R. Meyers, 2012, Seeing Red in Cyclic Stratigraphy: Spectral Noise Estimation for Astrochronology: Paleoceanography, 27, PA3228, doi:10.1029/2012PA002307.

Rahim, K.J. and Burr W.S. and Thomson, D.J., 2014, Appendix A: Multitaper R package in "Applications of Multitaper Spectral Analysis to Nonstationary Data", PhD diss., Queen's Univieristy, pp 149-183. http://hdl.handle.net/1974/12584

Thomson, D. J., 1982, Spectrum estimation and harmonic analysis, Proc. IEEE, 70, 1055-1096, doi:10.1109/PROC.1982.12433.

See Also

eha, lowspec, mtm, mtmAR, mtmML96, and periodogram

astrochron documentation built on Sept. 30, 2024, 9:14 a.m.