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

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`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) |

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.

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`

, `mtmAR`

, `mtmML96`

, `periodogram`

, and `spec.mtm`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
# 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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