Multitaper Method (MTM) Spectral Analysis with Power Law (1/f) fit
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)
Stratigraphic series for MTM spectral analysis. First column should be location (e.g., depth), second column should be data value.
MTM time-bandwidth product.
Number of DPSS tapers to use. By default, this is set to (2*tbw)-1.
Pad with zeros to (padfac*npts) points, where npts is the original number of data points.
Remove mean from data series? (T or F)
Remove linear trend from data series? (T or F)
Significance level for peak identification.
Lowest frequency to include in 1/f fit
Highest frequency to include in 1/f fit
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)
Plot power law noise confidence levels on power spectrum (in addition to the power law fit)? (T or F)
Smallest frequency for plotting.
Largest frequency for plotting.
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
Identify signficant frequencies on power and probabilty plots? (T or F)
Generate summary plots? (T or F)
Verbose output? (T or F)
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.
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.
eha, lowspec, mtm, mtmAR, mtmML96, and periodogram