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Multitaper.jl Documentation

Documentation for Multitaper.jl

A package for multitaper frequency-domain analysis.

Package Features

When doing exploratory analysis of time series, frequency domain methods, that is, statistical methods that display information about the temporal correlations of one or more time series in terms of frequencies, can be used to infer physical mechanisms for underlying process dynamics in e.g. geophysical time series, medical time series, etc.). The multitaper method, which leverages Slepian functions to estimate power spectral densities, coherences, and so forth, is implemented here for application to univariate, multivariate, and higher-dimensional (e.g. space-time) processes.

Multitaper.jl is a Julia package for spectrum analysis of time series, multivariate time series, and spatial or space-time processes. Multitaper.jl was designed to be useful to researchers in diverse fields, including geophysics (climate, seismology, limnology, and stratigraphy), cognitive radio, space science (solar physics), speech processing, astronomy, and biomedicine. For example, a researcher might want to compute the multitaper spectrum of a time series so he or she can identify which periodic components contribute the most to signal variance, and do so with jackknifed error bounds on the oscillation amplitudes.

Univariate time series

  • Discrete Prolate Spheroidal sequences (Slepian 1974) and with gaps (Chave 2019)

  • Multitaper spectra that use dpss (multispec) tapers, where time series can have gaps.

  • Jackknifing for estimation of the confidence intervals.

  • F-test for line components (Thomson, 1982).

  • Complex demodulation

  • Multitaper spectrum estimation for time series with equal temporal spacing except with gaps (Chave 2019)

Multivariate time series

  • Magnitude squared coherence, implemented in the spirit of Thomson and Chave, 1991.

  • Jackknife estimates of phase, unwrapped, similar to R's implementation.

  • T-squared test (Thomson, "Some comments on possibly cyclostationary series", Asilomar Conference Proceedings) for simultaneous line components.

2 Dimensional

  • 2 Dimensional Cartesian tapers supported on the square in space and 2D disk in time as described in Simons and Wang, 2011

Plots Recipes

Plots recipes are provided for numerous function ouputs.

The Examples provides tutorial IJulia.jl notebooks showing how to get started using Multitaper.

See the Index for the complete list of documented functions and types.

Installation

This package is unregistered, so please install with

Pkg> add https://github.com/lootie/Multitaper.jl.git

This package runs on Julia v 1.4.2 and above.

Testing

In order to test this package, use

Pkg> test Multitaper

This will run the tests in test/runtests.jl.

Manual

Index