Function index

The multitaper spectrum is given as a MTSpectrum structure which holds

• frequency (f),
• spectrum (S),
• phase (optional),
• chosen values of the multitaper time bandwidth product etc of type MTParameters (params)
• eigencoefficients (coef, optional),
• Ftest values (Fpval, optional),
• jackknife output (jkvar, optional), and
• Tsquared test results (Tsq_pval, optional).

The multitaper coherence structure, MTCoherence, holds

• frequency (f),
• coherence (coh),
• phase (phase),
• eigencoefficients (coef, optional),
• jackknife output (jkvar, optional), and
• Tsquared test results (Tsq, optional).

The multitaper transfer function is given as a MTTransferFunction structure which holds

• frequency (f),
• transfer function (transf),
• phase (phase),
• MTParameters (params),
• eigencoefficients (EigenCoefficientfs, optional),
• jackknife output (jkvar, optional), and
• Tsquared test results (Tsq, optional).

The EigenCoefficient structure holds

• multitaper eigencoefficients (coef) and, optionally,
• adaptive weights (wts)

Multitaper parameters MTParameters struct contains

• time bandwidth (NW) as Float,
• number of tapers (K),
• number of samples (N),
• sampling rate (dt) in temporal units (e.g. seconds),
• padded length (M),
• number of segments (nsegments), and
• overlap if nsegments is greater than 1, nothing otherwise.

Multitaper complex demodulates are held in the Demodulate struct which contains

• magnitude (Mag),
• phase (Phase)

The multitaper autocorrelation function is given in the MTAutocorrelationFunction structure which holds

• lags (lags),
• autocorrelation function (acf),
• MTParameters (params)

The multitaper autocovariance function is given in the MTAutocovarianceFunction structure, which holds

• lags (lags),
• autocovariance function (acvf),
• MTParameters (params)

The multitaper cepstrum is given in the MTCepstrum structure which holds

• lags (lags),
• cepstrum (ceps),
• MTParameters (params)

The multitaper cross-covariance function is given in the MtCrossCovarianceFunction structure which holds

• lags (lags),
• cross-covariance function (acvf),
• MTParameters (params)

The multitaper cross-correlation function is given as a MTCrossCorrelationFunction structure which holds

• lags (lags),
• cross-correlation function (acf),
• MTParameters (params)

dpss_tapers(n,w,k,tap_or_egval)

Simply compute discrete prolate spheroidal sequence tapers, eigenvalues

...

Arguments

• n::Int64: Length of the taper

• nw::Float64: Time-bandwidth product

• k::Int64: Number of tapers

• tap_or_egval::Symbol = :tap: Either :tap, :egval, or :both

...

...

Outputs

• vv::Vector{Float64}: The matrix of eigenvalues, if taporegval is set to :tap

• dpss_eigval: Struct conaining the dpss tapers

...

mdslepian(w, k, t)

Generalized prolate spheroidal sequences for the 1D missing data problem

...

Arguments

Positional Arguments

• w::Float64: the bandwidth

• k::Int64: number of Slepian tapers, must be <=2bwlength(x)

• t::Vector{Int64}: vector containing the time indices

...

...

Outputs

• lambda,u::Tuple{Vector{Float64}, Vector{Float64}}: tuple containing the

concentrations and the tapers

...

See also: mdmultispec, gpss

gpss(w, k, t, f; <keyword arguments>)

Generalized prolate spheroidal sequences on an unequal grid

...

Arguments

Positional Arguments

• w::Float64: the bandwidth

• k::Int64: number of Slepian tapers, must be <=2bwlength(x)

• t::Vector{Int64}: vector containing the time indices

• f::Float64: frequency at which the tapers are to be computed

Keyword Arguments

• beta::Float64 = 0.5: analysis half-bandwidth (similar to Nyquist rate)

...

...

Outputs

• lambda::Vector{Float64} the concentrations of the generalized prolate spheroidal

sequences

• u::Matrix{Float64} the matrix containing the sequences themselves

• R the Cholesky factor for the generalized eigenvalue problem

...

See also: gpss_orth, mdmultispec, mdslepian

multispec(S1; <keyword arguments>)

Computes univariate multitaper spectra with a handful of extra gadgets.

...

Arguments

• S1::Vector{T} where T<:Float64: the vector containing the time series
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed
• egval::Union{Vector{Float64},Nothing} = nothing: Vector of concentratins of said dpss's
• guts::Bool = false: whether or not to return the eigencoefficients in the output struct
• a_weight::Bool = true: whether or not to use adaptive weighting
• Ftest::Bool = true: Compute the F-test p-value
• highres::Bool = false: Whether to return a "high resolution" spectrum estimate
• jk::Bool = true: Compute jackknifed confidence intervals
• Tsq::Union{Vector{Int64},Vector{Vector{Int64}},Nothing} = nothing: which frequency indices to compute the T-squared test for multiple line components. Defaults to none.

...

...

Outputs

• MTSpectrum struct containing the spectrum

...

See also: dpss_tapers, MTSpectrum, mdmultispec, mdslepian

multispec(S1, S2; <keyword arguments>)

Computes multitaper cross-spectrum or coherence when given two time series with same sampling.

...

Arguments

• S1::Union{Vector{T},EigenCoefficient} where T<:Number: the vector containing the first time

series

• S2::Union{Vector{P},EigenCoefficient} where P<:Number: the vector containing the second

time series

• outp::Symbol: output can be either :coh for coherence, :spec for cross-spectrum,

or :transf for transfer function

• NW::Float64 = 4.0: time-bandwidth product of estimate

• K::Int64 = 6: number of slepian tapers, must be <= 2*NW

• offset::Union{Float64,Int64} = 0 set to nonzero value if offset coherence or

cross-spectrum is desired. If Float64 is used, this will be converted to nearest FFT bin.

• dt::Float64: sampling rate in time units

• ctr::Bool: whether or not to remove the mean before computing the multitaper

spectrum

• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will

be pad times length of the time series.

• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have

been precomputed

• guts::Bool = false: whether or not to return the eigencoefficients in the output

struct

• jk::Bool = true: Compute jackknifed confidence intervals

• Tsq::Union{Vector{Int64},Vector{Vector{Int64}},Nothing} = nothing: which

frequency indices to compute the T-squared test for multiple line components. Defaults to none.

• alph::Float64 = 0.05: significance cutoff for the Tsquared test

...

...

Outputs

• MTSpectrum, MTCoherence, or MTTransferFunction struct containing the spectrum, coherence or

transfer function, depending on the selection of outp input.

...

See also: dpss_tapers, MTSpectrum, mdmultispec, mdslepian

multispec(S1; <keyword arguments>)

Multivariate version of the multispec call, data are in the columns of a matrix ...

Arguments

• S1::Matrix{T} where T<:Float64: the vector containing the first time series
• outp::Symbol: output can be either :coh for coherence, :justspeccs to compute just the spectra, or :cross for cross-spectra
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed
• guts::Bool = false: whether or not to return the eigencoefficients in the output struct
• a_weight::Bool = true: whether or not to adaptively weight the spectra
• jk::Bool = false: Compute jackknifed confidence intervals
• Ftest:Bool = false: Compute F-test for line components
• Tsq::Union{Vector{Int64},Vector{Vector{Int64}},Nothing} = nothing: which frequency indices to compute the T-squared test for multiple line components. Defaults to none.
• alph::Float64 = 0.05: significance cutoff for the Tsquared test

...

...

Outputs

• Tuple{Vector{MTSpectrum},Vector{P},Union{Float64,Vector{Float64}}} where P = Union{MTCoherence,MTSpectrum}

struct containing the spectra, coherence or crossspectra, and Tsquared test p-values. Ouput of middle arg depends on the selection of outp input. ...

See also: dpss_tapers, MTSpectrum, mdmultispec, mdslepian

mdmultispec(tt, x; <keyword arguments>)

Multitaper power spectrum estimation for time series with missing data (gaps)

...

Arguments

Positional Arguments

• tt::Vector{T} where T<:Real: the vector containing the time indices

• x::Vector{P} where P<:Number: data vector

Keyword Arguments

• bw = 5/length(tt): bandwidth of estimate

• k::Int64 = 2*bw*length(x)-1: number of Slepian tapers, must be `<=

2bwlength(x)`

• dt::T = tt[2]-tt[1]: sampling rate in time units

• nz = 0.0: zero padding factor

• Ftest::Bool = true: Compute the F-test p-value

• jk::Bool = true: Compute jackknifed confidence intervals

• dof::Bool = false: Compute degrees of freedom for the adaptively weighted

spectrum estimate

• lambdau::Union{Tuple{Array{Float64,1},Array{Float64,2}},Nothing} = nothing:

Slepians, if precomputed ...

...

Outputs

• pkg::MTSpectrum struct containing the spectrum

• nu1::Vector{Float64} optional vector containing the degrees of freedom, given

if the dof kwarg is set to true.

...

See also: multispec, mdslepian

mdmultispec(tt, x, y; <keyword arguments>)

Multitaper coherence estimation for time series with missing data (gaps)

...

Arguments

Positional Arguments

• tt::Vector{T} where T<:Real: the vector containing the time indices

• x::Vector{P} where P<:Number: data vector 1

• y::Vector{Q} where Q<:Number: data vector 2

Keyword Arguments

• bw = 5/length(tt): bandwidth of estimate

• k::Int64 = 2*bw*length(x)-1: number of Slepian tapers, must be `<=

2bwlength(x)`

• dt = tt[2]-tt[1]: sampling rate in time units

• nz = 0.0: zero padding factor

• Ftest::Bool = true: Compute the F-test p-value

• jk::Bool = true: Compute jackknifed confidence intervals

• lambdau::Union{Tuple{Array{Float64,1},Array{Float64,2}},Nothing} = nothing:

Slepians, if precomputed

...

...

Outputs

• pkg::MTCoherence struct containing the coherence

...

See also: multispec, mdslepian

mdmultispec(tt, x; <keyword arguments>)

Multitaper coherence estimation for multiple time series with the same missing data (gaps)

...

Arguments

Keyword Arguments

• tt::Vector{T} where T<:Real: the vector containing the time indices

• x::Matrix{P} where P<:Number: time series in the columns of a matrix

Positional Arguments

• bw = 5/length(tt): bandwidth of estimate

• k::Int64 = 2*bw*length(x)-1: number of Slepian tapers, must be `<=

2bwlength(x)`

• dt = tt[2]-tt[1]: sampling rate in time units

• nz = 0.0: zero padding factor

• Ftest::Bool = false: Compute the F-test p-value

• jk::Bool = true: Compute jackknifed confidence intervals

• lambdau::Union{Tuple{Array{Float64,1},Array{Float64,2}},Nothing} = nothing:

Slepians, if precomputed

...

...

Outputs

• Tuple{Vector{MTSpectrum},Matrix{MTCoherence},Nothing} struct containing the spectra,

coherences, and T^2 test significances (currently set to return nothing)

...

See also: multispec, mdslepian

welch(S1, nsegments; <keyword arguments>)

Computes univariate multitaper Welch specrum starting with an input time series.

...

Arguments

• S1:Vector{T} where T<:Number: the vector containing the time series

• nsegments::Int64: the number of segments into which to divide the time series

• overlap::Float64 = 0.5: number between 0 and 1 which accounts for the amount of

overlap between the segments

• NW::Float64 = 4.0: time-bandwidth product of estimate

• K::Int64 = 6: number of slepian tapers, must be <= 2*NW

• dt::Float64: sampling rate in time units

• ctr::Bool: whether or not to remove the mean before computing the multitaper

spectrum

• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will

be pad times length of the time series.

• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have

been precomputed

• egval::Union{Vector{Float64},Nothing} = nothing: Vector of concentratins of said

dpss's

• guts::Bool = false: whether or not to return the eigencoefficients in the output

struct

• a_weight::Bool = true: whether or not to use adaptive weighting

...

...

Outputs

• MTSpectrum struct, depending on the selection of outp above

• Float64 containing the effective bandwidth

...

See also: multispec

mt_acf(S)

Computes univariate multitaper autocorrelation function. Inputs a MTSpectrum struct.

...

Arguments

• S::MTSpectrum: the vector containing the result of an univariate call to multispec

...

...

Outputs

• MTAutocorrelationFunction struct containing the autocorrelation function

...

See also: multispec

mt_acf(S1; <keyword arguments>)

Computes univariate multitaper autocorrelation function starting with an input time series. ...

Arguments

• S1::Vector{T} where T<:Number: the vector containing the time series
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed
• egval::Union{Vector{Float64},Nothing} = nothing: Vector of concentratins of said dpss's
• a_weight::Bool = true: whether or not to use adaptive weighting

...

...

Outputs

• MTAutocorrelationFunction struct containing the autocorrelation function

...

See also: multispec

mt_acvf(S)

Computes univariate multitaper autocovariance function. Inputs a MTSpectrum struct.

...

Arguments

• S::MTSpectrum: the vector containing the result of an univariate call to multispec

...

...

Outputs

• MTAutocovarianceFunction struct containing the autocovariance function.

...

See also: multispec

mt_acvf(S1; <keyword arguments>)

Computes univariate multitaper autocovariance function starting with an input time series. ...

Arguments

• S1::Vector{T} where T<:Number: the vector containing the time series
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed
• egval::Union{Vector{Float64},Nothing} = nothing: Vector of concentratins of said dpss's
• a_weight::Bool = true: whether or not to use adaptive weighting

...

...

Outputs

• MTAutocovarianceFunction struct containing the autocovariance function

...

See also: multispec

mt_ccvf(S; <keyword arguments>)

Computes univariate multitaper cross-covariance/cross-correlation function. Inputs a MTSpectrum struct.

...

Arguments

• S::MTSpectrum: the vector containing the result of an multiivariate call to multispec
• typ::Symbol = :ccvf: whether to compute cross-correlation function (:ccf) or cross-covariance function (:ccvf)

...

...

Outputs

• MtCrossCovarianceFunction, MTCrossCorrelationFunction depending on the selection of typ input above.

...

See also: multispec

mt_ccvf(S1, S2; <keyword arguments>)

Computes bivariate multitaper cross-covariance/cross-correlation function from two time series

...

Arguments

• S1::Vector{T} where T<:Number: the vector containing the first time series
• S2::Vector{T} where T<:Number: the vector containing the second time series
• typ::Symbol: whether to compute cross-covariance function (:ccvf), or cross-correlation function (:ccf)
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed

...

...

Outputs

• MtCrossCovarianceFunction struct, depending on the selection of typ input above.

...

See also: multispec

mt_cepstrum(S)

Computes multitaper cepstrum. Inputs a MTSpectrum struct.

...

Arguments

• S::MTSpectrum: the vector containing the result of an univariate call to multispec

...

...

Outputs

• MTCepstrum struct containing the cepstrum

...

See also: multispec

mt_cepstrum(S1; <keyword arguments>)

Computes multitaper cepstrum starting with an input time series. ...

Arguments

• S1::Vector{T} where T<:Number: the vector containing the time series
• NW::Float64 = 4.0: time-bandwidth product of estimate
• K::Int64 = 6: number of slepian tapers, must be <= 2*NW
• dt::Float64: sampling rate in time units
• ctr::Bool: whether or not to remove the mean before computing the multitaper spectrum
• pad::Float64 = 1.0: factor by which to pad the series, i.e. spectrum length will be pad times length of the time series.
• dpVec::Union{Matrix{Float64},Nothing} = nothing: Matrix of dpss's, if they have been precomputed
• egval::Union{Vector{Float64},Nothing} = nothing: Vector of concentratins of said dpss's
• a_weight::Bool = true: whether or not to use adaptive weighting

...

...

Outputs

• MTCepstrum struct containing the cepstrum

...

See also: multispec

demodulate(x, f0, NW, blockLen; <keyword arguments>)

Multitaper complex demodulation

...

Arguments

• x::Vector{T} where T<:Float64: the vector containing the time series
• f0::Float64: center frequency for the complex demodulate
• NW::Float64: the time bandwidth product
• blockLen::Int64: the length of the blocks to use
• wrapphase::Bool = true: whether or not to unwrap the phase
• dt::Float64 = 1.0: the sampling rate of the series, in time units
• basetime::Float64 = 0.0: the time at which the time series begins

...

...

Outputs

• A struct of type Demodulate

...

See also: Demodulate, and relevant plots recipe demodplot

tanhtrans(trcsq,ntf)

Inverse of the magnitude squared coherence variance stabilizing transform

...

Arguments

• trcsq::Float64: The transformed squared coherence
• ntf::Int64: the number of tapers use to compute the coherence

...

...

Outputs

• The output is a Float64 indicating the reverse-transformed MSC

...

Example

If the transformed coherence is 7.3 and 6 dof, the significance is

julia> invmscsig(tanhtrans(7.3,6),6)

If the significance is 0.9 and 6 dof the transformed msc is

julia> atanhtrans(sqrt(mscsig(0.9,6)),6)

See also: multispec

atanhtrans(c,ntf)

Magnitude squared coherence variance stabilizing transform

...

Arguments

• c::Float64: the value of the coherence
• ntf::Int64: the number of tapers use to compute the coherence

...

...

Outputs

• The output is a Float64 indicating the transformed MSC

...

See also: multispec

ejn(DoF)

Expected jackknife variance of an univariate multitaper spectrum estimate with DoF tapers

...

Arguments

• DoF::Int64: the number of tapers use to compute the spectrum

...

...

Outputs

• The output is a Float64 indicating the expected jackknife variance.

...

See also: multispec

unwrapphase(y, typ)

Unwrap the phase

...

Arguments

• y::Vector{Float64}: The vector of phases

• typ::Symbol: Whether to compute the unwrapped phase in degrees or radians

...

...

Outputs

• x::Vector{Float64}: The vector of unwrapped phases

...

Alternative phase unwrapper which takes a complex argument.

blockerr(lengt, nsegmentts; <keyword arguments>)

Blocker code to divide the data into segments

...

Arguments

• lengt::Int64: input length of a time series
• nsegments::Int64: number of segments
• overlap::Float64 = 0.0: fraction of overlap between segments, between 0.0 and 1.0

...

...

Outputs

• seq::Vector{Int64}: Beginning index for each segment
• seg_len::Int64: length of the segments
• ov::Float64: overlap that actually resulted (≈overlap, above)

...

Pgram_upcrossings(z, N)

Number of upcrossings of the level z of a periodogram spectrum per Rayleigh resolution ...

Arguments

• z::Float64: the level of the standardized spectrum
• N::Int64: sampling rate in time units

...

...

Outputs

• Float64: the number of upcrossings per Rayleigh

...

MT_Upcrossings(z, α, CR, N)

Number of upcrossings of the level z of a multitaper spectrum per Rayleigh resolution ...

Arguments

• z::Float64: the level of the standardized spectrum
• α::Float64: degrees of freedom of estimate
• `CR::Float64: time bandwidth product
• N::Int64: sampling rate in time units

...

...

Outputs

• Float64: the number of upcrossings per Rayleigh

...

Gives an upcrossing table for α = K, CR = NW (Float), optionally num_Ray has default 1e5, and signficiance levels that can be chosen, or set to default

rectsleps(nslep,n,m,Kp,N,M, <keyword arguments>)=)

Slepian functions concentrated in 2 dimensions on a rectangle in physical space and a circle in spectral space.

...

Arguments

• nslep::Int64: number of output slepians
• n::Int64: number of GL nodes in the x-direction
• m::Int64: number of GL nodes in the y-direction
• Kp::Float64: the radius of the circle in spectral space
• N::Int64: number of Gauss-Legendre nodes in the first dimension
• M::Int64: number of Gauss-Legendre nodes in the second dimension
• verbose::Boo: select true if you would like to see the concentrations

...

...

Outputs

• sleps::Array{Matrix{Float64},1} - an array of 2D tapers

...

multispec2_Rectangle(Md, K, ntaper; <keyword arguments>)

Function for computing the 2D multitaper spectrum estimate

...

Arguments

• Md::Matrix{T} where T<:Float64: data matrix
• K::Float64: squared radius (bandwidth) of the region of concentration in spectrum
• ntaper::Int64: number of tapers
• padn::Int64 = 0: number of samples to pad to in the x-direction
• padm::Int64 = 0: number of samples to pad to in the y-direction
• nquad::Int64 = 72: number of quadrature nodes in the x-direction
• mquad::Int64 = 72: number of quadrature nodes in the y-direction
• center::Bool = true: whether to subtract the mean or not
• sleps::Union{Matrix{T},Nothing} = nothing: if you have already computed the tapers, input them here

...

...

Outputs

• Matrix containing the 2D multitaper spectrum (simple averaging used)

Note: If this function runs slowly for the size of your input matrix, reducing the number of quadrature nodes for computing the tapers, or alternatively precomputing the tapers may help. ...

bspec(times, dat, W, K, beta, nz, Ftest)

Computes the Bronez spectrum of an unequally-spaced time series

...

Positional Arguments

• times::Vector{T} where T<: Number: the vector containing the times
• dat::Vector{T} where T<:Number: the vector containing the time series
• W::Float64: bandwidth of estimate
• K::Int64: number of slepian tapers, must be <= 2*NW
• beta::Float64: estimated process bandwidth (aka Nyquist rate)
• nz::Union{Float64,Int64} = length(t): Number of frequencies
• Ftest::Bool = false: Whether to compute the F-test or not

...

...

Outputs

• MTSpectrum struct containing the Bronez spectrum

...

...

Example usage

N = 256
t = collect(1:N).^(1.05)
W = 0.008
K = 5
x = randn(N)
bet = 0.5 / (last(t) / (N-1))
M = 2*N
S = bspec(t, x, W, K, bet, nz, true)

...

See also: multispec, mdmultispec, mdslepian, gpss

bspec(time, dat1, dat2, W, K, bet, nz; <keyword arguments>)

Computes the Bronez coherence or cross-spectrum of two unequally-spaced time series

...

Positional Arguments

• time::Vector{T} where T<:Number: the vector containing the times
• dat1::Union{Vector{P}, EigenCoefficient} where P<:Number: the vector containing the first time series
• dat2::Union{Vector{P}, EigenCoefficient} where P<:Number: the vector containing the second time series
• W::Float64: bandwidth of estimate
• K::Int64: number of slepian tapers, must be <= 2*NW
• bet::Float64: Nyquist frequency
• nz::Union{Float64,Int64} = length(t): Number of frequencies

Keyword Arguments

• outp::Symb = :coh: Output, either :cross for cross spectrum or :coh (default)
• params::Union{MTParameters,Nothing} = nothing: parameters struct, important when x,y are EigenCoefficients
• Ftest::Bool = false: Whether to compute the F-test or not

...

...

Outputs

• MTCoherence containing the Bronez coherence

...

...

Example usage

N = 256
t = collect(1:N).^(1.05)
W = 0.008
K = 5
x = randn(N)
y = randn(N) # Incoherent
M = 2*N
beta = 0.5
S = bspec(t, x, y, W, K, M, beta)

...

See also: multispec, mdmultispec, mdslepian, gpss

bspec(time, dat, W, K, bet, nz; <keyword arguments>)

Computes the Bronez spectra and coherences of p unequally-spaced time series

...

Positional Arguments

• time::Vector{T} where T<:Number: the vector containing the times
• dat::Matrix{Vector{P}} where T<:Number: the matrix containing the time series in its columns
• W::Float64: bandwidth of estimate
• K::Int64: number of slepian tapers, must be <= 2*NW
• bet::Float64: Nyquist frequency
• nz::Union{Float64,Int64} = length(t): Number of frequencies

Keyword Arguments

• outp::Symb = :coh: Output, either :cross for cross spectrum or :coh (default)
• Ftest::Bool = false: Whether to compute the F-test or not

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Outputs

• tuple(Vector{MTSpectrum},Matrix{MTCoherence},Nothing) containing the Bronez spectra and coherences

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Example usage

N = 256
t = collect(1:N).^(1.05)
W = 0.008
K = 5
x = randn(N)
y = randn(N) # Incoherent
M = 2*N
beta = 0.5
S = bspec(t, hcat(x, y), W, K, beta, M, outp = :coh, Ftest = true)

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See also: multispec, mdmultispec, mdslepian, gpss