Multitaper Method Spectral Analysis

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Description

Multitaper Method (MTM) Spectral Analysis (Thomson, 1982)

Usage

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mtm(dat,tbw=3,ntap=NULL,padfac=5,demean=T,detrend=F,siglevel=0.9,ar1=T,output=0,
     CLpwr=T,xmin,xmax,pl=1,sigID=T,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. (0-1)

ar1

Estimate conventional AR(1) noise spectrum and confidence levels? (T or F)

CLpwr

Plot AR(1) noise confidence levels on power spectrum? (T or F)

output

What should be returned as a data frame? (0=nothing; 1= power spectrum + harmonic CL + AR1 CL + AR1 fit + 90%-99% AR1 power levels (ar1 must be set to TRUE to output AR model results); 2=significant peak frequencies; 3=significant peak frequencies + harmonic CL; 4=internal variables from spec.mtm). Option 4 is intended for expert users, and should generally be avoided.

xmin

Smallest frequency for plotting.

xmax

Largest frequency for plotting.

pl

Plot logarithm of spectral power (1) or linear spectral power (2)?

sigID

Identify significant frequencies on power and probabilty plots? (T or F)

genplot

Generate summary plots? (T or F)

verbose

Verbose output? (T or F)

Details

If ar1=T, candidiate astronomical cycles are identified via isolation of those frequencies that achieve the required (e.g., 90 percent) "red noise" 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 red noise 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.

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, mtmAR, mtmML96, periodogram, and spec.mtm

Examples

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# generate example series with periods of 400 ka, 100 ka, 40 ka and 20 ka
ex = cycles(freqs=c(1/400,1/100,1/40,1/20),start=1,end=1000,dt=5)

# add AR1 noise
noise = ar1(npts=200,dt=5,sd=.5)
ex[2] = ex[2] + noise[2]

# MTM spectral analysis, with conventional AR1 noise test
pl(1,title="mtm")
mtm(ex,ar1=TRUE)

# compare to ML96 analysis
pl(1, title="mtmML96")
mtmML96(ex)

# compare to analysis with LOWSPEC
pl(1, title="lowspec")
lowspec(ex)

# compare to amplitudes from eha
pl(1,title="eha")
eha(ex,tbw=3,win=1000,pad=1000)

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