diff --git a/docs/src/periodograms.md b/docs/src/periodograms.md index 01587fa64..cf0136255 100644 --- a/docs/src/periodograms.md +++ b/docs/src/periodograms.md @@ -4,11 +4,33 @@ arraysplit periodogram(s::AbstractVector{T}) where T <: Number welch_pgram -mt_pgram spectrogram stft periodogram(s::AbstractMatrix{T}) where T <: Real freq power time +coherence +``` + +## Multitaper periodogram estimation + +```@docs +mt_pgram +mt_pgram! +mt_spectrogram +mt_spectrogram! +mt_cross_power_spectra +mt_cross_power_spectra! +mt_coherence +mt_coherence! +``` + +### Configuration objects + +```@docs +MTConfig +MTSpectrogramConfig +MTCrossSpectraConfig +MTCoherenceConfig ``` diff --git a/src/DSP.jl b/src/DSP.jl index bdc60ca76..a9bc52ee3 100644 --- a/src/DSP.jl +++ b/src/DSP.jl @@ -6,6 +6,11 @@ using IterTools: subsets export conv, deconv, filt, filt!, xcorr +# This function has methods added in `peridograms` but is not exported, +# so we define it here so one can do `DSP.allocate_output` instead of +# `DSP.Periodograms.allocate_output`. +function allocate_output end + include("dspbase.jl") include("util.jl") diff --git a/src/multitaper.jl b/src/multitaper.jl new file mode 100644 index 000000000..8c46086ff --- /dev/null +++ b/src/multitaper.jl @@ -0,0 +1,825 @@ +##### +##### Multitapered periodogram +##### + +struct MTConfig{T,R1,F,P,T1,T2,W,R2} + n_samples::Int + fs::R1 + nfft::Int + ntapers::Int + freq::F + plan::P + fft_input_tmp::T1 + fft_output_tmp::T2 + window::W + onesided::Bool + r::R2 # inverse normalization; e.g. equal to `fs*N` for an unwindowed/untapered periodogram of a signal of length `N` + # e.g. equal to `fs*ntapers*ones(ntapers)` when tapered by properly normalized window functions (i.e. norm-2 equal to 1 for each taper) + # can be adjusted to weight the tapers, e.g. by the eigenvalues of the DPSS windows + function MTConfig{T}(n_samples, nfft, ntapers, freq, fs, plan, fft_input_tmp, + fft_output_tmp, window, onesided, r) where {T} + n_samples > 0 || throw(ArgumentError("`n_samples` must be positive")) + nfft >= n_samples || throw(ArgumentError("Must have `nfft >= n_samples`")) + ntapers > 0 || throw(ArgumentError("`ntapers` must be positive")) + fs > 0 || throw(ArgumentError("`fs` must be positive")) + if size(plan) != size(fft_input_tmp) + throw(DimensionMismatch("""Must have `size(plan) == size(fft_input_tmp)`; + got `size(plan)` = $(size(plan)) and `size(fft_input_tmp)` = $(size(fft_input_tmp))""")) + end + if size(fft_input_tmp) != (nfft,) + throw(DimensionMismatch("""Must have `size(fft_input_tmp) == (nfft,)`; + got `size(fft_input_tmp)` = $(size(fft_input_tmp)) and `nfft` = $(nfft)""")) + end + if size(fft_output_tmp) != (length(freq),) + throw(DimensionMismatch("""Must have `size(fft_output_tmp) == (length(freq),)`; + got `size(fft_output_tmp)` = $(size(fft_output_tmp)) and `length(freq)` = $(length(freq))""")) + end + if size(window) != (n_samples, ntapers) + throw(DimensionMismatch("""Must have `size(window) == (n_samples, ntapers)`; + got `size(window)` = $(size(window)) and `(ntapers, n_samples)` = $((n_samples, ntapers))""")) + end + if size(r) != (ntapers,) + throw(DimensionMismatch("""Must have `size(r) == (ntapers,)`; + got `size(r)` = $(size(r)) and `(ntapers,)` = $((ntapers,))""")) + end + if onesided && T <: Complex + throw(ArgumentError("cannot compute one-sided FFT of a complex signal")) + end + return new{T,typeof(fs),typeof(freq),typeof(plan),typeof(fft_input_tmp), + typeof(fft_output_tmp),typeof(window),typeof(r)}(n_samples, fs, nfft, + ntapers, freq, plan, + fft_input_tmp, + fft_output_tmp, window, + onesided, r) + end +end + +# provides an `MTConfig` with `keep_only_large_evals` and `weight_by_evals` options used in some of the reference tests. +function dpss_config(::Type{T}, n_samples; nw=4, ntapers = 2nw-1, fs=1, keep_only_large_evals=false, + weight_by_evals=false, kwargs...) where {T} + + window = dpss(n_samples, nw, ntapers) + + if keep_only_large_evals + evals = dpsseig(window, nw) + keep_evals_mask = evals .> 0.9 + window = window[:, keep_evals_mask] + evals = evals[keep_evals_mask] + ntapers = size(window, 2) + else + evals = nothing + end + + if weight_by_evals + if evals === nothing + evals = dpsseig(window, nw) + end + taper_weights = evals ./ sum(evals) + else + taper_weights = fill(1/ntapers, ntapers) + end + + return MTConfig{T}(n_samples; window=window, nw=nw, ntapers=ntapers, taper_weights=taper_weights, fs=fs, kwargs...) +end + + +""" + MTConfig{T}(n_samples; fs=1, + nfft = nextpow(2, n_samples), + window = nothing, + nw = 4, + ntapers = 2 * nw - 1, + taper_weights = fill(1/ntapers, ntapers), + onesided::Bool=T<:Real, + fft_flags = FFTW.MEASURE) + +Creates a config object which holds the configuration state +and temporary variables used in multitaper computations, +e.g. [`mt_pgram!`](@ref), [`mt_spectrogram`](@ref), [`MTSpectrogramConfig`](@ref), +[`MTCrossSpectraConfig`](@ref), and [`MTCoherenceConfig`](@ref). + +An `MTConfig` can be re-used between computations as long +as none of the input arguments change. + +* `n_samples`: the number of samples to be used as input when computing multitaper periodograms + with this configuration. Used for pre-allocating temporary buffers. +* `fs`: the number of samples per second of the input signal +* `nfft`: length of input vector to the FFT; if `nfft > n_samples`, then the + input signal will be zero-padded until it is of length `nfft`. +* `window`: window function to use for tapering. If left at the default of `nothing`, + `window` will be set to `dpss(n_samples, nw, ntapers)`. +* `ntapers`: the number of tapers to use. +* `taper_weights = fill(1/ntapers, ntapers)`: how to weight the contribution of each taper. + The default setting is to simply average them. +* `onesided`: whether or not to compute a "one-sided" FFT by using that real signal data + yields conjugate-symmetry in Fourier space. +* `fft_flags`: flags to control how the FFT plan is generated. +""" +function MTConfig{T}(n_samples; fs=1, nfft=nextpow(2, n_samples), window=nothing, nw=4, + ntapers=2 * nw - 1, taper_weights = fill(1/ntapers, ntapers), + onesided::Bool=T <: Real, + fft_flags=FFTW.MEASURE) where {T} + if onesided && T <: Complex + throw(ArgumentError("cannot compute one-sided FFT of a complex signal")) + end + n_samples > 0 || throw(ArgumentError("`n_samples` must be positive")) + nfft >= n_samples || throw(ArgumentError("Must have `nfft >= n_samples`")) + freq = onesided ? rfftfreq(nfft, fs) : fftfreq(nfft, fs) + fft_input_tmp = Vector{T}(undef, nfft) + fft_output_tmp = Vector{fftouttype(T)}(undef, length(freq)) + plan = onesided ? plan_rfft(fft_input_tmp; flags=fft_flags) : + plan_fft(fft_input_tmp; flags=fft_flags) + if window === nothing + r = fs ./ taper_weights + window = dpss(n_samples, nw, ntapers) + else + r = fs .* vec(sum(abs2, window; dims=1)) ./ taper_weights + end + + return MTConfig{T}(n_samples, nfft, ntapers, freq, fs, plan, fft_input_tmp, + fft_output_tmp, window, onesided, r) +end + +function allocate_output(config::MTConfig{T}) where {T} + return Vector{fftabs2type(T)}(undef, length(config.freq)) +end + + +# Internal function used in [`mt_pgram!`](@ref) and [`mt_cross_power_spectra!`](@ref). +function mt_fft_tapered!(fft_output, signal, taper_index, config) + # Create the input: tapered + zero-padded version of the signal + fft_input = config.fft_input_tmp + @inbounds for i in 1:length(signal) + fft_input[i] = config.window[i, taper_index] * signal[i] + end + fft_input[(length(signal) + 1):(config.nfft)] .= 0 + + # do the FFT + mul!(fft_output, config.plan, fft_input) + return nothing +end + + +""" + mt_pgram(s; onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, nw=4, ntapers=iceil(2nw)-1, window=dpss(length(s), nw, ntapers)) + mt_pgram(signal::AbstractVector, config::MTConfig) + +Computes the multitaper periodogram of a signal `s`. + +If `window` is not specified, the signal is tapered with +`ntapers` discrete prolate spheroidal sequences with +time-bandwidth product `nw`. Each sequence is equally weighted; +adaptive multitaper is not (yet) supported. + +If `window` is specified, each column is applied as a taper. The +sum of periodograms is normalized by the total sum of squares of +`window`. + +Returns a `Periodogram`. + +See also [`mt_pgram!`](@ref) and [`MTConfig`](@ref). +""" +mt_pgram + +function mt_pgram(s::AbstractVector{T}; onesided::Bool=eltype(s)<:Real, + nfft::Int=nextfastfft(length(s)), fs::Real=1, + nw::Real=4, ntapers::Int=ceil(Int, 2nw)-1, + window::Union{AbstractMatrix,Nothing}=nothing) where T<:Number + config = MTConfig{T}(length(s); fs = fs, + nfft = nfft, window = window, nw = nw, ntapers = ntapers, onesided = onesided, + fft_flags = FFTW.ESTIMATE) + out = allocate_output(config) + return mt_pgram!(out, s, config) +end + +function mt_pgram!(output, s::AbstractVector{T}; onesided::Bool=eltype(s)<:Real, + nfft::Int=nextfastfft(length(s)), fs::Real=1, + nw::Real=4, ntapers::Int=ceil(Int, 2nw)-1, + window::Union{AbstractMatrix,Nothing}=nothing) where T<:Number + config = MTConfig{T}(length(s); fs = fs, + nfft = nfft, window = window, nw = nw, ntapers = ntapers, onesided = onesided, + fft_flags = FFTW.ESTIMATE) + return mt_pgram!(output, s, config) +end + +function mt_pgram(signal::AbstractVector, config::MTConfig) + out = allocate_output(config) + return mt_pgram!(out, signal, config) +end + +""" + mt_pgram!(output, s::AbstractVector{T}; onesided::Bool=eltype(s)<:Real, + nfft::Int=nextfastfft(length(s)), fs::Real=1, + nw::Real=4, ntapers::Int=ceil(Int, 2nw)-1, + window::Union{AbstractMatrix,Nothing}=nothing) where T<:Number + mt_pgram!(output::AbstractVector, signal::AbstractVector, config::MTConfig) -> Periodogram + +Computes a multitapered periodogram, storing the output in `output`. Arguments: + +* `signal::AbstractVector`: should be of length `config.n_samples` +* `output::AbstractVector`: should be of length `length(config.freq)` + +Optionally pass an [`MTConfig`](@ref) object to preallocate temporary variables +and choose configuration settings; otherwise, keyword arguments may be passed +to choose those settings. + +Returns a `Periodogram`. + +See also [`mt_pgram`](@ref) and [`MTConfig`](@ref). +""" +mt_pgram! + +function mt_pgram!(output::AbstractVector, signal::AbstractVector, config::MTConfig) + if length(output) != length(config.freq) + throw(DimensionMismatch("""Expected `output` to be of length `length(config.freq)`; + got `length(output) = $(length(output)) and `length(config.freq)` = $(length(config.freq))""")) + end + if length(signal) != config.n_samples + throw(DimensionMismatch("""Expected `signal` to be of length `config.n_samples`; + got `length(signal) == $(length(signal)) and `config.n_samples` = $(config.n_samples)""")) + end + fft_output = config.fft_output_tmp + + output .= 0 + for taper_index in 1:(config.ntapers) + mt_fft_tapered!(fft_output, signal, taper_index, config) + fft2pow!(output, fft_output, config.nfft, config.r[taper_index], config.onesided) + end + return Periodogram(output, config.freq) +end + +##### +##### Multitapered spectrogram +##### + +struct MTSpectrogramConfig{T,C<:MTConfig{T}} + n_samples::Int + n_overlap_samples::Int + time::FloatRange{Float64} + mt_config::C +end + +""" + MTSpectrogramConfig(n_samples, mt_config::MTConfig{T}, n_overlap_samples) where {T} + MTSpectrogramConfig{T}(n_samples, samples_per_window, n_overlap_samples; fs=1, kwargs...) where {T} + +Creates a `MTSpectrogramConfig` which holds configuration and temporary variables for [`mt_spectrogram`](@ref) and [`mt_spectrogram!`](@ref). +Any keyword arguments accepted by [`MTConfig`](@ref) may be passed here, or an `MTConfig` object itself. +""" +function MTSpectrogramConfig(n_samples::Int, mt_config::MTConfig{T}, n_overlap_samples::Int) where {T} + samples_per_window = mt_config.n_samples + if samples_per_window <= n_overlap_samples + throw(ArgumentError("Need `samples_per_window > n_overlap_samples`; got `samples_per_window` = $(samples_per_window) and `n_overlap_samples` = $(n_overlap_samples).")) + end + + f = samples_per_window / 2 + hop = samples_per_window - n_overlap_samples + + len = n_samples < samples_per_window ? 0 : div(n_samples - samples_per_window, samples_per_window - n_overlap_samples) + 1 + time = range(f, step = hop, length = len) / mt_config.fs + return MTSpectrogramConfig{T,typeof(mt_config)}(n_samples, n_overlap_samples, time, + mt_config) +end + +# add a method for if the user specifies the type, i.e. `MTSpectrogramConfig{T}` +function MTSpectrogramConfig{T}(n_samples::Int, mt_config::MTConfig{T}, n_overlap_samples::Int) where {T} + return MTSpectrogramConfig(n_samples, mt_config, n_overlap_samples) +end + +# Create the `MTConfig` if it's not passed +function MTSpectrogramConfig{T}(n_samples::Int, samples_per_window::Int, + n_overlap_samples::Int; fs=1, kwargs...) where {T} + return MTSpectrogramConfig(n_samples, MTConfig{T}(samples_per_window; fs=fs, kwargs...), n_overlap_samples) +end + +""" + mt_spectrogram!(output, signal::AbstractVector{T}, n::Int=length(signal) >> 3, + n_overlap::Int=n >> 1; fs::Int=1, onesided::Bool=T <: Real, kwargs...) where {T} + mt_spectrogram!(destination::AbstractMatrix, signal::AbstractVector, config::MTSpectrogramConfig) + +Computes a multitaper spectrogram using the parameters specified in `config`. Arguments: + +* `destination`: `length(config.mt_config.freq)` x `length(config.time)` matrix. This can be created by `DSP.allocate_output(config)`. +* `signal`: vector of length `config.n_samples` +* `config`: optionally, pass an [`MTSpectrogramConfig`](@ref) object to hold temporary variables and configuration settings. Otherwise, settings arguments may be passed directly. + +Returns a `Spectrogram`. + +See also [`mt_spectrogram`](@ref). +""" +mt_spectrogram! + +function mt_spectrogram!(output, signal::AbstractVector{T}, n::Int=length(signal) >> 3, + n_overlap::Int=n >> 1; fs::Int=1, onesided::Bool=T <: Real, + kwargs...) where {T} + config = MTSpectrogramConfig{T}(length(signal), n, n_overlap; fs=fs, onesided=onesided, + fft_flags=FFTW.ESTIMATE, kwargs...) + return mt_spectrogram!(output, signal, config) +end + +@views function mt_spectrogram!(destination::AbstractMatrix, signal::AbstractVector, + config::MTSpectrogramConfig) + if size(destination) != (length(config.mt_config.freq), length(config.time)) + throw(DimensionMismatch("""Expected `destination` to be of size `(length(config.mt_config.freq), length(config.time))`; + got `size(destination) == $(size(destination)) and + `(length(config.mt_config.freq), length(config.time))` = $((length(config.mt_config.freq), length(config.time)))""")) + end + if length(signal) != config.n_samples + throw(DimensionMismatch("""Expected `signal` to be of length `config.n_samples`; + got `length(signal) = $(length(signal)) and `config.n_samples` = $(config.n_samples)""")) + end + samples_per_window = config.mt_config.n_samples + subepochs = arraysplit(signal, samples_per_window, config.n_overlap_samples) + @assert length(subepochs) == length(config.time) + for (time_index, subepoch) in enumerate(subepochs) + mt_pgram!(destination[:, time_index], subepoch, config.mt_config) + end + return Spectrogram(destination, config.mt_config.freq, config.time) +end + +function allocate_output(config::MTSpectrogramConfig{T}) where {T} + return Matrix{fftabs2type(T)}(undef, length(config.mt_config.freq), length(config.time)) +end + +function mt_spectrogram(signal::AbstractVector, config::MTSpectrogramConfig) + output = allocate_output(config) + return mt_spectrogram!(output, signal, config) +end + +""" + mt_spectrogram(signal::AbstractVector{T}, n::Int=length(s) >> 3, + n_overlap::Int=n >> 1; fs::Int=1, + onesided::Bool=T <: Real, kwargs...) where {T} + mt_spectrogram(signal::AbstractVector, config::MTSpectrogramConfig) + +Compute a multitaper spectrogram, returning a `Spectrogram` object. +Optionally pass a [`MTSpectrogramConfig`](@ref) object; otherwise, any additional keyword +arguments accepted by [`MTConfig`](@ref) may be passed to configure the tapering. + +Returns a `Spectrogram`. + +See also [`mt_spectrogram!`](@ref). +""" +mt_spectrogram + +function mt_spectrogram(signal::AbstractVector{T}, n::Int=length(signal) >> 3, + n_overlap::Int=n >> 1; fs::Int=1, onesided::Bool=T <: Real, + kwargs...) where {T} + config = MTSpectrogramConfig{T}(length(signal), n, n_overlap; fs=fs, onesided=onesided, + fft_flags=FFTW.ESTIMATE, kwargs...) + X = allocate_output(config) + return mt_spectrogram!(X, signal, config) +end + + + + +""" + mt_spectrogram(signal::AbstractVector, mt_config::MTConfig, + n_overlap::Int=mt_config.n_samples >> 1) -> Spectrogram + +Compute a multitaper spectrogram using an an [`MTConfig`](@ref) object to choose +the window size. Note that all the workspace variables are contained in the [`MTConfig`](@ref) object, and this object can be re-used between spectrogram computations, so that only the output needs to be allocated. + +Returns a `Spectrogram`. + +See also [`mt_spectrogram!`](@ref). + +## Example + +```julia +signal1 = sin.(10_000) .+ randn(10_000) +mt_config = MTConfig{Float64}(1000) # 1000 samples per window +spec1 = mt_spectrogram(signal1, mt_config, 500) +signal2 = cos.(2_000) .+ randn(2_000) +spec2 = mt_spectrogram(signal2, mt_config, 250) # same `mt_config`, different signal, different overlap +``` +""" +function mt_spectrogram(signal::AbstractVector, mt_config::MTConfig{T}, + n_overlap::Int=mt_config.n_samples >> 1) where {T} + config = MTSpectrogramConfig{T}(length(signal), mt_config, n_overlap) + X = allocate_output(config) + return mt_spectrogram!(X, signal, config) +end + +##### +##### Multitapered cross spectral matrix +##### + +# the following code was initially ported from MNE-python before being partially rewritten. +# MNE-python's 3-clause BSD license can be found here: . + + +""" + CrossPowerSpectra{T,F,A<:AbstractArray{T, 3}} + +Access the power (an `n_channels` x `n_channels` x `length(freq)` array) via the function [`power`](@ref), and the frequencies by the function [`freq`](@ref). + +See also [`mt_cross_power_spectra`](@ref) and [`mt_cross_power_spectra!`](@ref). +""" +struct CrossPowerSpectra{T,F,A<:AbstractArray{T, 3}} + power::A + freq::F +end + +freq(c::CrossPowerSpectra) = c.freq +power(c::CrossPowerSpectra) = c.power + +function check_onesided_real(mt_config::MTConfig{T}) where T + if !((T <: Real) && mt_config.onesided) + throw(ArgumentError("Only real data is supported (with the default choice of `onesided=true`) for this operation.")) + end + return nothing +end + +struct MTCrossSpectraConfig{T,T1,T2,T3,T4,F,T5,T6,C<:MTConfig{T}} + n_channels::Int + normalization_weights::T1 + x_mt::T2 + demean::Bool + mean_per_channel::T3 + demeaned_signal::T4 + freq::F + freq_range::T5 + freq_inds::T6 + ensure_aligned::Bool + mt_config::C + function MTCrossSpectraConfig{T,T1,T2,T3,T4,F,T5,T6,C}(n_channels, normalization_weights, + x_mt, demean, mean_per_channel, demeaned_signal, freq, freq_range, + freq_inds, ensure_aligned, mt_config) where {T,T1,T2,T3,T4,F,T5,T6,C} + check_onesided_real(mt_config) # this restriction is artifical; the code needs to be generalized + return new{T,T1,T2,T3,T4,F,T5,T6,C}(n_channels, normalization_weights, x_mt, + demean, mean_per_channel, demeaned_signal, freq, freq_range, + freq_inds, ensure_aligned, mt_config) + end +end + +""" + MTCrossSpectraConfig{T}(n_channels, n_samples; fs=1, demean=false, freq_range=nothing, + ensure_aligned = T == Float32 || T == Complex{Float32}, kwargs...) where {T} + MTCrossSpectraConfig(n_channels, mt_config::MTConfig{T}; demean=false, freq_range=nothing, + ensure_aligned = T == Float32 || T == Complex{Float32}) + +Creates a configuration object used for [`mt_cross_power_spectra`](@ref) and [`mt_cross_power_spectra!`](@ref). + +* `n_channels`: the number of channels of the input. +* `n_samples`: the number of samples for each channel of the input. +* `demean`: if `true`, the channelwise mean will be subtracted from the input signals before the cross spectral powers are computed. +* `freq_range`: if `nothing`, all frequencies are retained. Otherwise, only frequencies between `first(freq_range)` and `last(freq_range)` are retained. +* `ensure_aligned = T == Float32 || T == Complex{Float32}`: perform an extra copy to ensure that the FFT output is memory-aligned +* Additionally, either pass an [`MTConfig`](@ref) object, or keyword arguments such as `fs` accepted by [`MTConfig`](@ref). + +Returns a `CrossPowerSpectra` object. +""" +function MTCrossSpectraConfig{T}(n_channels, n_samples; fs=1, demean=false, + freq_range=nothing, + ensure_aligned = T == Float32 || T == Complex{Float32}, + kwargs...) where {T} + mt_config = MTConfig{T}(n_samples; fs=fs, kwargs...) + return MTCrossSpectraConfig{T}(n_channels, mt_config; demean=demean, freq_range=freq_range, ensure_aligned=ensure_aligned) +end + +# extra method to ensure it's ok to pass the redundant type parameter {T} +MTCrossSpectraConfig{T}(n_channels, mt_config::MTConfig{T}; demean=false, + freq_range=nothing, ensure_aligned = T == Float32 || T == Complex{Float32}) where {T} = MTCrossSpectraConfig(n_channels, mt_config; demean=demean, + freq_range=freq_range, ensure_aligned = ensure_aligned) + +function MTCrossSpectraConfig(n_channels, mt_config::MTConfig{T}; demean=false, + freq_range=nothing, ensure_aligned = T == Float32 || T == Complex{Float32}) where {T} + + n_samples = mt_config.n_samples + if demean + mean_per_channel = Vector{T}(undef, n_channels) + demeaned_signal = Matrix{T}(undef, n_channels, n_samples) + else + mean_per_channel = nothing + demeaned_signal = nothing + end + + normalization_weights = 2 ./ mt_config.r + + x_mt = Array{fftouttype(T),3}(undef, length(mt_config.freq), mt_config.ntapers, + n_channels) + if freq_range !== nothing + freq_mask = first(freq_range) .< mt_config.freq .< last(freq_range) + freq_inds = findall(freq_mask) + freq = mt_config.freq[freq_mask] + else + freq_inds = eachindex(mt_config.freq) + freq = mt_config.freq + end + return MTCrossSpectraConfig{T,typeof(normalization_weights),typeof(x_mt), + typeof(mean_per_channel),typeof(demeaned_signal), + typeof(freq),typeof(freq_range),typeof(freq_inds), + typeof(mt_config)}(n_channels, normalization_weights, x_mt, demean, + mean_per_channel, demeaned_signal, freq, + freq_range, freq_inds, ensure_aligned, mt_config) +end + +function allocate_output(config::MTCrossSpectraConfig{T}) where {T} + return Array{fftouttype(T),3}(undef, config.n_channels, config.n_channels, + length(config.freq)) +end + +""" + mt_cross_power_spectra!(output, signal::AbstractMatrix; fs=1, kwargs...) + mt_cross_power_spectra!(output, signal::AbstractMatrix, config::MTCrossSpectraConfig) + +Computes multitapered cross power spectra between channels of a signal. Arguments: + +* `output`: `n_channels` x `n_channels` x `length(config.freq)`. Can be created by `DSP.allocate_output(config)`. +* `signal`: `n_channels` x `n_samples` +* `config`: `MTCrossSpectraConfig{T}`: optionally pass a [`MTCrossSpectraConfig`](@ref) to + preallocate temporary and choose configuration settings. + Otherwise, one may pass any keyword arguments accepted by this object. + +Produces a `CrossPowerSpectra` object holding the `n_channels` x `n_channels` x `n_frequencies` +output array and the corresponding frequencies (accessed by [`freq`](@ref)). + +See also [`mt_cross_power_spectra`](@ref) and [`MTCrossSpectraConfig`](@ref). +""" +mt_cross_power_spectra! + +function mt_cross_power_spectra!(output, signal::AbstractMatrix{T}; fs=1, kwargs...) where {T} + n_channels, n_samples = size(signal) + config = MTCrossSpectraConfig{T}(n_channels, n_samples; fs=fs, fft_flags=FFTW.ESTIMATE, + kwargs...) + return mt_cross_power_spectra!(output, signal, config) +end + +@views function mt_cross_power_spectra!(output, signal::AbstractMatrix, + config::MTCrossSpectraConfig) + if size(signal) != (config.n_channels, config.mt_config.n_samples) + throw(DimensionMismatch("Size of `signal` does not match `(config.n_channels, config.mt_config.n_samples)`; + got `size(signal)`=$(size(signal)) but `(config.n_channels, config.mt_config.n_samples)`=$((config.n_channels, config.mt_config.n_samples))")) + end + if size(output) != (config.n_channels, config.n_channels, length(config.freq_inds)) + throw(DimensionMismatch("Size of `output` does not match `(config.n_channels, config.n_channels, length(config.freq_inds))`; + got `size(output)`=$(size(output)) but `(config.n_channels, config.n_channels, length(config.freq_inds))`=$((config.n_channels, config.n_channels, length(config.freq_inds)))")) + end + + if config.demean + mean!(config.mean_per_channel, signal) + config.demeaned_signal .= signal .- config.mean_per_channel + signal = config.demeaned_signal + end + + x_mt = config.x_mt + + if config.ensure_aligned + mt_fft_tapered_multichannel_ensure_aligned!(x_mt, signal, config) + else + mt_fft_tapered_multichannel!(x_mt, signal, config) + end + x_mt[1, :, :] ./= sqrt(2) + if iseven(config.mt_config.nfft) + x_mt[end, :, :] ./= sqrt(2) + end + cs_inner!(output, config.normalization_weights, x_mt, config) + return CrossPowerSpectra(output, config.freq) +end + +function mt_fft_tapered_multichannel_ensure_aligned!(x_mt, signal, config) + fft_output = config.mt_config.fft_output_tmp + for k in 1:(config.n_channels), taper in 1:config.mt_config.ntapers + # we do this in two steps so that we are sure `fft_output` has the memory alignment FFTW expects (without needing the `FFTW.UNALIGNED` flag) + mt_fft_tapered!(fft_output, signal[k, :], taper, config.mt_config) + x_mt[:, taper, k] .= fft_output + end +end + +@views function mt_fft_tapered_multichannel!(x_mt, signal, config) + for k in 1:(config.n_channels), taper in 1:config.mt_config.ntapers + mt_fft_tapered!(x_mt[:, taper, k], signal[k, :], taper, config.mt_config) + end +end + +function cs_inner!(output, normalization_weights, x_mt, config) + freq_inds = config.freq_inds + n_channels = config.n_channels + @boundscheck checkbounds(output, 1:n_channels, 1:n_channels, 1:length(freq_inds)) + @boundscheck checkbounds(normalization_weights, 1:length(normalization_weights)) + @boundscheck checkbounds(x_mt, freq_inds, 1:length(normalization_weights), 1:n_channels) + output .= zero(eltype(output)) + # Up to the `normalization_weights` scaling, we have + # J_k^l(f) = x_mt[k, f, l] + # Ŝ^lm(f) = output[l, m, f] + # using the notation from https://en.wikipedia.org/wiki/Multitaper#The_method + # so the formula `Ŝ^lm(f) = \sum_k conj(J_k^l(f)) * (J_k^m(f))`` becomes the following loop: + @inbounds for (fi, f) in enumerate(freq_inds), + m in 1:n_channels, + l in 1:n_channels, + k in 1:length(normalization_weights) + + output[l, m, fi] += normalization_weights[k] * x_mt[f, k, l] * conj(x_mt[f, k, m]) + end + return nothing +end + +""" + mt_cross_power_spectra(signal::AbstractMatrix{T}; fs=1, kwargs...) where {T} + mt_cross_power_spectra(signal::AbstractMatrix, config::MTCrossSpectraConfig) + +Computes multitapered cross power spectra between channels of a signal. Arguments: + +* `signal`: `n_channels` x `n_samples` +* Optionally pass an [`MTCrossSpectraConfig`](@ref) object to preallocate temporary variables +and choose configuration settings. Otherwise, any keyword arguments accepted by [`MTCrossSpectraConfig`](@ref) may be passed here. + +Produces a `CrossPowerSpectra` object holding the `n_channels` x `n_channels` x `n_frequencies` +output array (accessed by [`power`](@ref)) and the corresponding frequencies (accessed by [`freq`](@ref)). + +See also [`mt_cross_power_spectra!`](@ref) and [`MTCrossSpectraConfig`](@ref). +""" +mt_cross_power_spectra + +function mt_cross_power_spectra(signal::AbstractMatrix{T}; fs=1, kwargs...) where {T} + n_channels, n_samples = size(signal) + config = MTCrossSpectraConfig{T}(n_channels, n_samples; fs=fs, fft_flags=FFTW.ESTIMATE, + kwargs...) + return mt_cross_power_spectra(signal, config) +end + +function mt_cross_power_spectra(signal::AbstractMatrix, config::MTCrossSpectraConfig) + output = allocate_output(config) + return mt_cross_power_spectra!(output, signal, config) +end + +##### +##### Multitapered coherences +##### + +struct MTCoherenceConfig{T,T1,C<:MTCrossSpectraConfig{T}} + cs_matrix::T1 + cs_config::C +end + +""" + MTCoherenceConfig{T}(n_channels, n_samples; fs=1, demean=false, freq_range=nothing, kwargs...) where T + MTCoherenceConfig(cs_config::MTCrossSpectraConfig{T}) where {T} + MTCoherenceConfig(n_channels, mt_config::MTConfig{T}; demean=false, freq_range=nothing, + ensure_aligned = T == Float32 || T == Complex{Float32}) where {T} + +Creates a configuration object for coherences from a [`MTCrossSpectraConfig`](@ref). Provides a helper method +with the same arugments as `MTCrossSpectraConfig` to construct the `MTCrossSpectraConfig` object. + +See also [`mt_coherence`](@ref) and [`mt_coherence!`](@ref). +""" +function MTCoherenceConfig(cs_config::MTCrossSpectraConfig{T}) where {T} + cs_matrix = allocate_output(cs_config) + return MTCoherenceConfig{T,typeof(cs_matrix),typeof(cs_config)}(cs_matrix, cs_config) +end + +# add a method to cover the case in which the user specifies the `{T}` here +MTCoherenceConfig{T}(cs_config::MTCrossSpectraConfig{T}) where {T} = MTCoherenceConfig(cs_config) + +function MTCoherenceConfig{T}(n_channels, n_samples; fs=1, demean=false, + freq_range=nothing, kwargs...) where {T} + cs_config = MTCrossSpectraConfig{T}(n_channels, n_samples; fs=fs, demean=demean, + freq_range=freq_range, kwargs...) + cs_matrix = allocate_output(cs_config) + return MTCoherenceConfig{T,typeof(cs_matrix),typeof(cs_config)}(cs_matrix, cs_config) +end + +# ensure it's OK to pass the extra {T} type parameter +function MTCoherenceConfig{T}(n_channels, mt_config::MTConfig{T}; demean=false, + freq_range=nothing, ensure_aligned = T == Float32 || T == Complex{Float32}) where T + return MTCoherenceConfig(n_channels, mt_config; demean=demean, + freq_range=freq_range, ensure_aligned = ensure_aligned) +end + +function MTCoherenceConfig(n_channels, mt_config::MTConfig{T}; demean=false, + freq_range=nothing, ensure_aligned = T == Float32 || T == Complex{Float32}) where {T} + cs_config = MTCrossSpectraConfig(n_channels, mt_config; demean=demean, + freq_range=freq_range, ensure_aligned=ensure_aligned) + cs_matrix = allocate_output(cs_config) + return MTCoherenceConfig{T,typeof(cs_matrix),typeof(cs_config)}(cs_matrix, cs_config) +end + + +function allocate_output(config::MTCoherenceConfig{T}) where {T} + return Array{real(T)}(undef, config.cs_config.n_channels, config.cs_config.n_channels, length(config.cs_config.freq)) +end + +""" + coherence_from_cs!(output::AbstractArray, cs_matrix) + +Compute the pairwise channel coherences from a cross spectral matrix, storing the result in `output`. +""" +function coherence_from_cs!(output::AbstractArray{T}, cs_matrix) where T + n_channels = size(cs_matrix, 2) + n_freqs = size(cs_matrix, 3) + @boundscheck checkbounds(output, 1:n_channels, 1:n_channels, 1:n_freqs) + @boundscheck checkbounds(cs_matrix, 1:n_channels, 1:n_channels, 1:n_freqs) + output .= zero(T) + @inbounds for ch2 in 1:n_channels + for ch1 in (ch2 + 1):n_channels # lower triangular matrix + for f in 1:n_freqs + output[ch1, ch2, f] += abs(cs_matrix[ch1, ch2, f]) / + sqrt(real(cs_matrix[ch1, ch1, f] * + cs_matrix[ch2, ch2, f])) + end + end + end + output .+= PermutedDimsArray(output, (2, 1, 3)) # symmetrize + # diagonal elements should be `1` for any frequency + @inbounds for i in 1:n_channels + output[i, i, :] .= one(T) + end + return nothing +end + +""" + Coherence + +Holds an `n_channels` x `n_channels` x `length(freq)` array consisting of the pairwise coherences between each channel for each frequency which is accessed by [`coherence`](@ref), as well +as the frequencies accessed by [`freq`](@ref). + +See also [`mt_coherence`](@ref) and [`mt_coherence!`](@ref). +""" +struct Coherence{T,F,A<:AbstractArray{T, 3}} + coherence::A + freq::F +end + +freq(c::Coherence) = c.freq + +""" + coherence(c::Coherence) + +Given an `Coherence` object, returns an `n_channels` x `n_channels` x `length(freq(c))` +array consisting of the pairwise coherences between each channel for each frequency. +""" +coherence(c::Coherence) = c.coherence + +""" + mt_coherence!(output, signal::AbstractMatrix; fs=1, freq_range=nothing, demean=false, kwargs...) + mt_coherence!(output, signal::AbstractMatrix, config::MTCoherenceConfig) + +Computes the pairwise coherences between channels. + +* `output`: `n_channels` x `n_channels` matrix +* `signal`: `n_samples` x `n_channels` matrix +* `config`: optional configuration object that pre-allocates temporary variables and choose settings. + +Returns a `Coherence` object. + +See also [`mt_coherence`](@ref) and [`MTCoherenceConfig`](@ref). +""" +mt_coherence! + +function mt_coherence!(output, signal::AbstractMatrix, + config::MTCoherenceConfig) + if size(signal) != (config.cs_config.n_channels, config.cs_config.mt_config.n_samples) + throw(DimensionMismatch("Size of `signal` does not match `(config.cs_config.n_channels, config.cs_config.mt_config.n_samples)`; + got `size(signal)`=$(size(signal)) but `(config.cs_config.n_channels, config.cs_config.mt_config.n_samples)`=$((config.cs_config.n_channels, config.cs_config.mt_config.n_samples))")) + end + if size(output) != (config.cs_config.n_channels, config.cs_config.n_channels, length(config.cs_config.freq)) + throw(DimensionMismatch("Size of `output` does not match `(config.cs_config.n_channels, config.cs_config.n_channels, length(config.cs_config.freq))`; + got `size(output)`=$(size(output)) but `(config.cs_config.n_channels, config.cs_config.n_channels, length(config.cs_config.freq))`=$((config.cs_config.n_channels, config.cs_config.n_channels, length(config.cs_config.freq)))")) + end + cs = mt_cross_power_spectra!(config.cs_matrix, signal, config.cs_config) + coherence_from_cs!(output, power(cs)) + + return Coherence(output, config.cs_config.freq) +end + +function mt_coherence!(output, signal::AbstractMatrix{T}; fs=1, freq_range=nothing, demean=false, + kwargs...) where {T} + n_channels, n_samples = size(signal) + config = MTCoherenceConfig{T}(n_channels, n_samples; fs=fs, demean=demean, + freq_range=freq_range, + fft_flags=FFTW.ESTIMATE, kwargs...) + return mt_coherence!(output, signal, config) +end + + +""" + mt_coherence(signal::AbstractMatrix{T}; fs=1, freq_range = nothing, demean=false, kwargs...) where T + mt_coherence(signal::AbstractMatrix, config::MTCoherenceConfig) + +Arguments: + +* `signal`: `n_channels` x `n_samples` matrix +* Optionally pass an `MTCoherenceConfig` to pre-allocate temporary variables and choose configuration settings, otherwise, see [`MTCrossSpectraConfig`](@ref) for the meaning of the keyword arguments. + +Returns a `Coherence` object. + +See also [`mt_coherence`](@ref) and [`MTCoherenceConfig`](@ref). +""" +mt_coherence + +function mt_coherence(signal::AbstractMatrix{T}; fs=1, freq_range=nothing, demean=false, + kwargs...) where {T} + n_channels, n_samples = size(signal) + config = MTCoherenceConfig{T}(n_channels, n_samples; fs=fs, demean=demean, + freq_range=freq_range, + fft_flags=FFTW.ESTIMATE, kwargs...) + return mt_coherence(signal, config) +end + + +function mt_coherence(signal::AbstractMatrix, config::MTCoherenceConfig) + cohs = allocate_output(config) + return mt_coherence!(cohs, signal, config) +end diff --git a/src/periodograms.jl b/src/periodograms.jl index b33d4718e..5cba85c1a 100644 --- a/src/periodograms.jl +++ b/src/periodograms.jl @@ -3,11 +3,17 @@ module Periodograms using LinearAlgebra: mul! using ..Util, ..Windows -export arraysplit, nextfastfft, periodogram, welch_pgram, mt_pgram, - spectrogram, power, freq, stft +using Statistics: mean! +export arraysplit, nextfastfft, periodogram, welch_pgram, + spectrogram, power, freq, stft, + MTConfig, mt_pgram, mt_pgram!, + MTSpectrogramConfig, mt_spectrogram, mt_spectrogram!, + MTCrossSpectraConfig, mt_cross_power_spectra, mt_cross_power_spectra!, + MTCoherenceConfig, mt_coherence, mt_coherence!, + coherence +import ..DSP: allocate_output using FFTW import FFTW: Frequencies, fftfreq, rfftfreq - ## ARRAY SPLITTER struct ArraySplit{T<:AbstractVector,S,W} <: AbstractVector{Vector{S}} @@ -22,7 +28,7 @@ struct ArraySplit{T<:AbstractVector,S,W} <: AbstractVector{Vector{S}} # n = noverlap is a problem - the algorithm will not terminate. (0 ≤ noverlap < n) || error("noverlap must be between zero and n") nfft >= n || error("nfft must be >= n") - new{Ti,Si,Wi}(s, zeros(Si, nfft), n, noverlap, window, div((length(s) - n), n - noverlap)+1) + new{Ti,Si,Wi}(s, zeros(Si, nfft), n, noverlap, window, length(s) >= n ? div((length(s) - n), n - noverlap)+1 : 0) end end ArraySplit(s::AbstractVector, n, noverlap, nfft, window) = @@ -62,7 +68,7 @@ Base.collect(x::ArraySplit) = collect(copy(a) for a in x) ## UTILITY FUNCTIONS # Convert the output of an FFT to a PSD and add it to out -function fft2pow!(out::Array{T}, s_fft::Vector{Complex{T}}, nfft::Int, r::Real, onesided::Bool, offset::Int=0) where T +function fft2pow!(out::AbstractArray{T}, s_fft::AbstractVector{Complex{T}}, nfft::Int, r::Real, onesided::Bool, offset::Int=0) where T m1 = convert(T, 1/r) n = length(s_fft) if onesided @@ -184,12 +190,12 @@ end ## PERIODOGRAMS abstract type TFR{T} end -struct Periodogram{T,F<:Union{Frequencies,AbstractRange}} <: TFR{T} - power::Vector{T} +struct Periodogram{T,F<:Union{Frequencies,AbstractRange}, V <: AbstractVector{T}} <: TFR{T} + power::V freq::F end -struct Periodogram2{T,F1<:Union{Frequencies,AbstractRange},F2<:Union{Frequencies,AbstractRange}} <: TFR{T} - power::Matrix{T} +struct Periodogram2{T,F1<:Union{Frequencies,AbstractRange},F2<:Union{Frequencies,AbstractRange}, M<:AbstractMatrix{T}} <: TFR{T} + power::M freq1::F1 freq2::F2 end @@ -197,21 +203,24 @@ end """ power(p) -For a Periodogram, returns the computed power at each frequency as +For a `Periodogram`, returns the computed power at each frequency as a Vector. -For a Spectrogram, returns the computed power at each frequency and +For a `Spectrogram`, returns the computed power at each frequency and time bin as a Matrix. Dimensions are frequency × time. + +For a `CrossPowerSpectra`, returns the pairwise power between each pair +of channels at each frequency. Dimensions are channel x channel x frequency. """ power(p::TFR) = p.power """ freq(p) -Returns the frequency bin centers for a given Periodogram or -Spectrogram object. +Returns the frequency bin centers for a given `Periodogram`, +`Spectrogram`, `CrossPowerSpectra`, or `Coherence` object. -Returns a tuple of frequency bin centers for a given Periodogram2 +Returns a tuple of frequency bin centers for a given `Periodogram2` object. """ freq(p::TFR) = p.freq @@ -381,62 +390,14 @@ function welch_pgram(s::AbstractVector{T}, n::Int=length(s)>>3, noverlap::Int=n> Periodogram(out, onesided ? rfftfreq(nfft, fs) : fftfreq(nfft, fs)) end -""" - mt_pgram(s; onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, nw=4, ntapers=iceil(2nw)-1, window=dpss(length(s), nw, ntapers)) - -Computes the multitaper periodogram of a signal `s`. - -If `window` is not specified, the signal is tapered with -`ntapers` discrete prolate spheroidal sequences with -time-bandwidth product `nw`. Each sequence is equally weighted; -adaptive multitaper is not (yet) supported. - -If `window` is specified, each column is applied as a taper. The -sum of periodograms is normalized by the total sum of squares of -`window`. - -See also: [`dpss`](@ref) -""" -function mt_pgram(s::AbstractVector{T}; onesided::Bool=eltype(s)<:Real, - nfft::Int=nextfastfft(length(s)), fs::Real=1, - nw::Real=4, ntapers::Int=ceil(Int, 2nw)-1, - window::Union{AbstractMatrix,Nothing}=nothing) where T<:Number - onesided && T <: Complex && error("cannot compute one-sided FFT of a complex signal") - nfft >= length(s) || error("nfft must be >= n") - - if isa(window, Nothing) - window = dpss(length(s), nw, ntapers) - r::T = fs*ntapers - else - size(window, 1) == length(s) || - error(DimensionMismatch("length of signal $(length(s)) must match first dimension of window $(size(window,1))")) - r = fs*sum(abs2, window) - end - - out = zeros(fftabs2type(T), onesided ? (nfft >> 1)+1 : nfft) - input = zeros(fftintype(T), nfft) - tmp = Vector{fftouttype(T)}(undef, T<:Real ? (nfft >> 1)+1 : nfft) - - plan = forward_plan(input, tmp) - for j = 1:size(window, 2) - for i = 1:size(window, 1) - @inbounds input[i] = window[i, j]*s[i] - end - mul!(tmp, plan, input) - fft2pow!(out, tmp, nfft, r, onesided) - end - - Periodogram(out, onesided ? rfftfreq(nfft, fs) : fftfreq(nfft, fs)) -end - ## SPECTROGRAM @static if isdefined(Base, :StepRangeLen) const FloatRange{T} = StepRangeLen{T,Base.TwicePrecision{T},Base.TwicePrecision{T}} end -struct Spectrogram{T,F<:Union{Frequencies,AbstractRange}} <: TFR{T} - power::Matrix{T} +struct Spectrogram{T,F<:Union{Frequencies,AbstractRange}, M<:AbstractMatrix{T}} <: TFR{T} + power::M freq::F time::FloatRange{Float64} end @@ -508,4 +469,6 @@ function stft(s::AbstractVector{T}, n::Int=length(s)>>3, noverlap::Int=n>>1, out end +include("multitaper.jl") + end # end module definition diff --git a/test/data/csd_array_multitaper_frequencies.txt b/test/data/csd_array_multitaper_frequencies.txt new file mode 100644 index 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MTSpectrogramConfig{Float64}(n_samples, n_samples_per_window, n_overlap) + @test length(config.time) == length(arraysplit(1:n_samples, n_samples_per_window, n_overlap)) + end + + @testset "`MTConfig` inner constructor errors" begin + n_samples = 100 + nfft = 200 + ntapers = 5 + fs = 1 + window = rand(n_samples, ntapers) + for T in (Float32, Float64, Complex{Float32}, Complex{Float64}) + fft_input_tmp = Vector{T}(undef, nfft) + onesided = T <: Real + fft_flags = FFTW.ESTIMATE + freqs = onesided ? rfftfreq(nfft, fs) : fftfreq(nfft, fs) + fft_output_tmp = Vector{fftouttype(T)}(undef, length(freqs)) + r = fs*ntapers*ones(ntapers) + plan = onesided ? plan_rfft(fft_input_tmp; flags=fft_flags) : + plan_fft(fft_input_tmp; flags=fft_flags) + # Test that the current configuation is valid so we know if it errors later + # it's because we changed it, not that it was always broken + @test MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) isa MTConfig + # now do a series of changes (in let-blocks to introduce new local bindings) + # and check that they are each invalid + let n_samples = 201 + @test_throws ArgumentError MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let n_samples = -1 + @test_throws ArgumentError MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let ntapers = -1 + @test_throws ArgumentError MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let fs = -1 + @test_throws ArgumentError MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let fft_input_tmp = Vector{T}(undef, 2*nfft) + @test_throws DimensionMismatch MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let nfft = 2*nfft, fft_input_tmp = Vector{T}(undef, 2*nfft) + @test_throws DimensionMismatch MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let window = rand(2*ntapers, n_samples) + @test_throws DimensionMismatch MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + let r = 1.0 + @test_throws DimensionMismatch MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + if T <: Complex + let onesided=true, freqs=rfftfreq(nfft, fs), fft_output_tmp=Vector{fftouttype(T)}(undef, length(freqs)), plan=plan_fft(fft_input_tmp; flags=fft_flags) + @test_throws ArgumentError MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) + end + end + # let's check that our original config is still valid, meaning we haven't + # accidentally broken the config by not properly scoping our changes + # (and therefore invalidating the tests that follow). + @test MTConfig{T}(n_samples, nfft, ntapers, freqs, fs, plan, fft_input_tmp, fft_output_tmp, window, onesided, r) isa MTConfig + end + end + +end + +@testset "`dpss_config`" begin + dpss_config = DSP.Periodograms.dpss_config(Float64, 1024; keep_only_large_evals=false, weight_by_evals=false) + mt_config = MTConfig{Float64}(1024) + + @test dpss_config.window ≈ mt_config.window + @test dpss_config.ntapers == mt_config.ntapers + @test dpss_config.r ≈ mt_config.r + + dpss_config = DSP.Periodograms.dpss_config(Float64, 1024; keep_only_large_evals=false, weight_by_evals=true) + @test dpss_config.window ≈ mt_config.window + @test dpss_config.ntapers == mt_config.ntapers + # should be different since we're weighting by eigenvalues now + @test sum(abs, dpss_config.r - mt_config.r) > 0.1 +end + +avg_coh(x) = dropdims(mean(coherence(x); dims=3); dims=3) + +@testset "Coherence (synthetic data)" begin + fs = 1000.0 + n_samples = 1024 + t = (0:1023) ./ fs + sin_1 = sin.(2 * π * 12.0 * t) # 12 Hz sinusoid signal + sin_2 = sin.(2 * π * 12.0 * t .+ π) + noise = rand(1024) * 2 .- 1 + + same_signal = Matrix{Float64}(undef, 2, n_samples) + same_signal[1, :] = sin_1 + same_signal[2, :] = sin_1 + coh = avg_coh(mt_coherence(same_signal; demean=true, fs=fs, freq_range = (10, 15))) + same_signal_coherence = coh[2,1] + + # test in-place gets the same result + config = MTCoherenceConfig{eltype(same_signal)}(size(same_signal)...; demean=true, fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + coh2 = avg_coh(mt_coherence!(out, same_signal, config)) + @test coh ≈ coh2 + + # check that the output object has the right frequency information and properties + coh_object = mt_coherence!(out, same_signal, config) + @test freq(coh_object) == coh_object.freq == config.cs_config.freq + @test all(x -> 10 <= x <= 15, freq(coh_object)) + # Check symmetries + for i in 1:2, j in 1:2, f in eachindex(freq(coh_object)) + @test coherence(coh_object)[i, j, f] == coherence(coh_object)[j, i, f] + if i == j + @test coherence(coh_object)[i,j, f] == 1 + end + end + + # check that manually demeaning with `demean=false` gives the same result + same_signal_demeaned = same_signal .- mean(same_signal; dims = 2) + coh3 = avg_coh(mt_coherence(same_signal_demeaned; demean = false)) + @test coh3 ≈ coh2 + + + @test_throws DimensionMismatch mt_coherence!(zeros(size(out,1), 2*size(out, 2), size(out, 3)), same_signal, config) + @test_throws DimensionMismatch mt_coherence!(out, vcat(same_signal, same_signal), config) + + + @test abs(same_signal_coherence - 1) < epsilon + + phase_shift = Matrix{Float64}(undef, 2, n_samples) + phase_shift[1, :] = sin_1 + phase_shift[2, :] = sin_2 + coh = avg_coh(mt_coherence(phase_shift; fs=fs, freq_range = (10, 15))) + phase_shift_coherence = coh[2,1] + @test abs(phase_shift_coherence - 1) < epsilon + @test coh[1,1] ≈ 1 + @test coh[2,2] ≈ 1 + + # test in-place gets the same result + config = MTCoherenceConfig{eltype(phase_shift)}(size(phase_shift)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + coh2 = avg_coh(mt_coherence!(out, phase_shift, config)) + @test coh ≈ coh2 + + # test out-of-place with config the same result + config = MTCoherenceConfig{eltype(phase_shift)}(size(phase_shift)...; fs=fs, freq_range = (10, 15)) + coh3 = avg_coh(mt_coherence(phase_shift, config)) + @test coh ≈ coh3 + + # test in-place without config the same result + coh4 = avg_coh(mt_coherence!(out, phase_shift; fs=fs, freq_range = (10, 15))) + @test coh ≈ coh4 + + # Construct the config via an `MTConfig` + mt_config = MTConfig{eltype(phase_shift)}(size(phase_shift, 2); fs=fs) + config = MTCoherenceConfig(size(phase_shift, 1), mt_config; freq_range = (10, 15)) + coh5 = avg_coh(mt_coherence(phase_shift, config)) + @test coh ≈ coh5 + + # Construct the config via an `MTCrossSpectraConfig` + config = MTCoherenceConfig(MTCrossSpectraConfig(size(phase_shift, 1), mt_config; freq_range = (10, 15))) + coh5 = avg_coh(mt_coherence(phase_shift, config)) + @test coh ≈ coh5 + + different_signal = Matrix{Float64}(undef, 2, n_samples) + different_signal[1, :] = sin_1 + different_signal[2, :] = noise + coh = avg_coh(mt_coherence(different_signal; fs=fs, freq_range = (10, 15))) + different_signal_coherence = coh[2,1] + # .8 is arbitrary, but represents a high coherence, so if a sine wave is + # that coherent with noise, there is a problem + @test different_signal_coherence < 0.8 + + # test in-place gets the same result + config = MTCoherenceConfig{eltype(different_signal)}(size(different_signal)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + coh2 = avg_coh(mt_coherence!(out, different_signal, config)) + @test coh ≈ coh2 + + less_noisy = Matrix{Float64}(undef, 2, n_samples) + less_noisy[1, :] = sin_1 + less_noisy[2, :] .= sin_1 .+ noise + coh = avg_coh(mt_coherence(less_noisy; fs=fs, freq_range = (10, 15))) + less_noisy_coherence = coh[2, 1] + + # test in-place gets the same result + config = MTCoherenceConfig{eltype(less_noisy)}(size(less_noisy)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + coh2 = avg_coh(mt_coherence!(out, less_noisy, config)) + @test coh ≈ coh2 + + more_noisy = Matrix{Float64}(undef, 2, n_samples) + more_noisy[1, :] = sin_1 + more_noisy[2, :] .= sin_1 .+ 3 * noise + coh = avg_coh(mt_coherence(more_noisy; fs=fs, freq_range = (10, 15))) + more_noisy_coherence = coh[2, 1] + @test less_noisy_coherence < same_signal_coherence + @test more_noisy_coherence < less_noisy_coherence + @test different_signal_coherence < more_noisy_coherence + + # test in-place gets the same result + config = MTCoherenceConfig{eltype(more_noisy)}(size(more_noisy)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + coh2 = avg_coh(mt_coherence!(out, more_noisy, config)) + @test coh ≈ coh2 + + several_signals = Matrix{Float64}(undef, 3, n_samples) + several_signals[1, :] = sin_1 + several_signals[2, :] = sin_2 + several_signals[3, :] = noise + several_signals_coherences = avg_coh(mt_coherence(several_signals; fs=fs, freq_range = (10, 15))) + @test length(several_signals_coherences) == 9 + @test several_signals_coherences[2, 1] ≈ phase_shift_coherence + @test several_signals_coherences[3, 1] ≈ different_signal_coherence + + # test in-place gets the same result + config = MTCoherenceConfig{Float64}(size(several_signals)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + @test eltype(out) == Float64 + coh2 = avg_coh(mt_coherence!(out, several_signals, config)) + @test coh2 ≈ several_signals_coherences + + # Float32 output: + config = MTCoherenceConfig{Float32}(size(several_signals)...; fs=fs, freq_range = (10, 15)) + out = allocate_output(config) + @test eltype(out) == Float32 + coh3 = avg_coh(mt_coherence!(out, several_signals, config)) + @test coh3 ≈ several_signals_coherences + + # Float32 input and output: + coh4 = avg_coh(mt_coherence!(out, Float32.(several_signals), config)) + @test coh4 ≈ several_signals_coherences +end + +@testset "`mt_coherence` reference test" begin + fs = 1000.0 + n_samples = 1024 + t = (0:1023) ./ fs + sin_1 = sin.(2 * π * 12.0 * t) # 12 Hz sinusoid signal + sin_2 = sin.(2 * π * 12.0 * t .+ π) + noise = vec(readdlm(joinpath(@__DIR__, "data", "noise.txt"))) # generated by `rand(1024) * 2 .- 1` + more_noisy = Array{Float64}(undef, 1, 2, n_samples) + more_noisy[1, 1, :] = sin_1 + more_noisy[1, 2, :] .= sin_1 .+ 3 * noise + + ## to generate the reference result: + # using PyMNE + # mne_coherence_matrix, _ = PyMNE.connectivity.spectral_connectivity(more_noisy, method="coh",sfreq=fs,mode="multitaper",fmin=10,fmax=15,verbose=false) + # coh = dropdims(mean(mne_coherence_matrix; dims=3); dims=3)[2, 1] + coh = 0.982356762670818 + + mt_config = DSP.Periodograms.dpss_config(Float64, n_samples; fs=fs, keep_only_large_evals=true, weight_by_evals=true) + config = MTCoherenceConfig(2, mt_config; freq_range = (10,15), demean=true) + result = avg_coh(mt_coherence(dropdims(more_noisy;dims=1), config)) + @test result[2, 1] ≈ coh +end + +@testset "`mt_cross_power_spectra`" begin + fs = 1000.0 + n_samples = 1024 + t = (0:1023) ./ fs + data = Array{Float64, 3}(undef, 1, 2, n_samples) + data[1,1,:] = sin.(2 * π * 12.0 * t) # 12 Hz sinusoid signal + data[1,2,:] = sin.(2 * π * 12.0 * t .+ π) + ## Script to generate reference data: + # using PyMNE, DelimitedFiles + # result = PyMNE.time_frequency.csd_array_multitaper(data, fs, n_fft = nextpow(2, n_samples), low_bias=true, adaptive=false) + # csd_array_multitaper_frequencies = result.frequencies + # csd_array_multitaper_values = reduce((x,y) -> cat(x,y; dims=3), [ r.get_data() for r in result]) + # writedlm("data/csd_array_multitaper_frequencies.txt", csd_array_multitaper_frequencies) + # writedlm("data/csd_array_multitaper_values_re.txt", real(csd_array_multitaper_values)) + # writedlm("data/csd_array_multitaper_values_im.txt", imag(csd_array_multitaper_values)) + csd_array_multitaper_frequencies = readdlm(joinpath(@__DIR__, "data", "csd_array_multitaper_frequencies.txt")) + csd_array_multitaper_values_re = reshape(readdlm(joinpath(@__DIR__, "data", "csd_array_multitaper_values_re.txt")), (2,2,512)) + csd_array_multitaper_values_im = reshape(readdlm(joinpath(@__DIR__, "data", "csd_array_multitaper_values_im.txt")), (2,2,512)) + csd_array_multitaper_values = csd_array_multitaper_values_re + im*csd_array_multitaper_values_im + + signal = dropdims(data; dims=1) + mt_config = DSP.Periodograms.dpss_config(Float64, n_samples; fs=fs, keep_only_large_evals=true, weight_by_evals=true) + config = MTCrossSpectraConfig(2, mt_config; demean=true) + result = mt_cross_power_spectra(signal, config) + @test signal isa Matrix{Float64} + @test freq(result)[2:end] ≈ csd_array_multitaper_frequencies + @test power(result)[:,:,2:end] ≈ csd_array_multitaper_values + + # Test in-place. Full precision: + config = MTCrossSpectraConfig(size(signal, 1), mt_config; demean=true) + out = allocate_output(config) + @test eltype(out) == Complex{Float64} + result2 = mt_cross_power_spectra!(out, signal, config) + @test freq(result) ≈ freq(result2) + @test power(result) ≈ power(result2) + + # Float32 output: + mt_config32 = DSP.Periodograms.dpss_config(Float32, n_samples; fs=fs, keep_only_large_evals=true, weight_by_evals=true) + config = MTCrossSpectraConfig(size(signal, 1), mt_config32; demean=true) + out = allocate_output(config) + @test eltype(out) == Complex{Float32} + result2 = mt_cross_power_spectra!(out, signal, config) + @test freq(result2) ≈ freq(result) + @test power(result2) ≈ power(result) + + # Float32 input and output: + result3 = mt_cross_power_spectra!(out, Float32.(signal), config) + @test freq(result3) ≈ freq(result) + @test power(result3) ≈ power(result) + + @test_throws DimensionMismatch mt_cross_power_spectra!(similar(out, size(out, 1) + 1, size(out, 2), size(out, 3)), signal, config) + @test_throws DimensionMismatch mt_cross_power_spectra!(out, vcat(signal, signal), config) + +end + + +@testset "`mt_cross_power_spectra` agrees with `mt_pgram`" begin + fs = 1000.0 + n_samples = 1024 + t = (0:1023) ./ fs + noise = vec(readdlm(joinpath(@__DIR__, "data", "noise.txt"))) + signal = sin.(2 * π * 12.0 * t) .+ 3 * noise + cs = mt_cross_power_spectra(reshape(signal, 1, :); fs=fs) + p = mt_pgram(signal; fs=fs) + + @test freq(cs) ≈ freq(p) + @test dropdims(power(cs); dims=(1,2)) ≈ power(p) + + # out-of-place with config + config = MTCrossSpectraConfig{Float64}(1, length(signal); fs=fs) + cs = mt_cross_power_spectra(reshape(signal, 1, :), config) + @test freq(cs) ≈ freq(p) + @test dropdims(power(cs); dims=(1,2)) ≈ power(p) + + # in-place without config + out = allocate_output(config) + cs = mt_cross_power_spectra!(out, reshape(signal, 1, :); fs=fs) + @test freq(cs) ≈ freq(p) + @test dropdims(power(cs); dims=(1,2)) ≈ power(p) + + # rm once two-sided FFTs supported + @test_throws ArgumentError mt_cross_power_spectra(reshape(complex.(signal), 1, :); fs=fs) +end diff --git a/test/periodograms.jl b/test/periodograms.jl index 4d651b25d..bfc8d2bbf 100644 --- a/test/periodograms.jl +++ b/test/periodograms.jl @@ -30,6 +30,68 @@ using FFTW: fftfreq @test p0 ≈ p @test f0 ≈ f @test t0 ≈ t + + + mt_spec = mt_spectrogram(x0, 256, 128; fs=10) + @test freq(mt_spec) == f + @test time(mt_spec) == t + @test power(mt_spec)[:,1] ≈ power(mt_pgram(x0[1:256]; fs=10)) + + # in-place full precision version: + spec_config = MTSpectrogramConfig{Float64}(length(x0), 256, 128; fs=10) + out = allocate_output(spec_config) + mt_spec2 = mt_spectrogram!(out, x0, spec_config) + @test power(mt_spec2) ≈ power(mt_spec) + @test freq(mt_spec2) == freq(mt_spec) + @test time(mt_spec2) == time(mt_spec) + + # out-of-place with config: + r = mt_spectrogram(x0, spec_config) + @test power(r) ≈ power(mt_spec) + @test freq(r) == freq(mt_spec) + @test time(r) == time(mt_spec) + + # in-place without config: + r = mt_spectrogram!(out, x0, 256, 128; fs=10) + @test power(r) ≈ power(mt_spec) + @test freq(r) == freq(mt_spec) + @test time(r) == time(mt_spec) + + # in-place half precision version: + spec_config = MTSpectrogramConfig{Float32}(length(x0), 256, 128; fs=10) + out = allocate_output(spec_config) + mt_spec3 = mt_spectrogram!(out, x0, spec_config) + @test power(mt_spec3) ≈ power(mt_spec) + @test freq(mt_spec3) == freq(mt_spec) + @test time(mt_spec3) == time(mt_spec) + + mt_spec4 = mt_spectrogram!(out, Float32.(x0), spec_config) + @test power(mt_spec4) ≈ power(mt_spec) + @test freq(mt_spec4) == freq(mt_spec) + @test time(mt_spec4) == time(mt_spec) + + # We can also only pass the window config. Full precision: + config = MTConfig{Float64}(256; fs=10) + mt_spec5 = mt_spectrogram(x0, config, 128) + @test power(mt_spec5) ≈ power(mt_spec) + @test freq(mt_spec5) == freq(mt_spec) + @test time(mt_spec5) == time(mt_spec) + + # We can also only pass the window config. Half precision: + config = MTConfig{Float32}(256; fs=10) + mt_spec6 = mt_spectrogram(x0, config, 128) + @test power(mt_spec6) ≈ power(mt_spec) + @test freq(mt_spec6) == freq(mt_spec) + @test time(mt_spec6) == time(mt_spec) + + # with Float32 input: + mt_spec7 = mt_spectrogram(Float32.(x0), config, 128) + @test power(mt_spec7) ≈ power(mt_spec) + @test freq(mt_spec7) == freq(mt_spec) + @test time(mt_spec7) == time(mt_spec) + + @test_throws DimensionMismatch mt_spectrogram!(similar(out, size(out, 1), size(out, 2)+1), x0, spec_config) + @test_throws DimensionMismatch mt_spectrogram!(out, vcat(x0, x0), spec_config) end @testset "0:7" begin @@ -309,4 +371,91 @@ end @assert isa(x, Vector) @test pointer(x) == pointer(q.buf) end + + x = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_x.txt"))) + @test eltype(x) <: Float64 + + # MATLAB code: + # fft = 2^nextpow2(length(x)); + # [pxx,fx] = pmtm(x,4,nfft,1000,'unity'); + fx = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_fx.txt"))) + pxx = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_pxx.txt"))) + + fs = 1000 + nw=4 + nfft = nextpow(2, length(x)) + result = mt_pgram(x; fs=fs, nw=nw, nfft=nfft) + @test freq(result) ≈ fx + @test power(result) ≈ pxx + + # Test against in-place. Full precision: + config = MTConfig{Float64}(length(x); fs=fs, nw=nw, nfft=nfft) + out = allocate_output(config) + @test eltype(out) == Float64 + result2 = mt_pgram!(out, x, config) + @test freq(result2) ≈ fx + @test power(result2) ≈ pxx + + # in-place without config + r = mt_pgram!(out, x; fs=fs, nw=nw, nfft=nfft) + @test freq(r) ≈ fx + @test power(r) ≈ pxx + + # out-of-place with config + r = mt_pgram(x, config) + @test freq(r) ≈ fx + @test power(r) ≈ pxx + + # Lower precision output: + config = MTConfig{Float32}(length(x); fs=fs, nw=nw, nfft=nfft) + out = allocate_output(config) + @test eltype(out) == Float32 + result3 = mt_pgram!(out, x, config) + @test freq(result3) ≈ fx + @test power(result3) ≈ pxx + + # with Float32 input: + result4 = mt_pgram!(out, Float32.(x), config) + @test freq(result4) ≈ fx + @test power(result4) ≈ pxx + + @test_throws DimensionMismatch mt_pgram!(similar(out, length(out)+1), x, config) + @test_throws DimensionMismatch mt_pgram!(out, vcat(x, one(eltype(x))), config) + + y = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_y.txt"))) + z = x + im*y + @test eltype(z) <: Complex{Float64} + + # MATLAB code: `[pzz,fz] = pmtm(z,4,nfft,1000, 'unity')` + fz = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_fz.txt"))) + pzz = vec(readdlm(joinpath(dirname(@__FILE__), "data", "pmtm_pzz.txt"))) + result = mt_pgram(z; fs=fs, nw=nw, nfft=nfft) + result_mask = 0 .< freq(result) .< 500 + freqs = freq(result)[result_mask] + @test freqs ≈ fz[2:length(freqs)+1] + @test power(result)[result_mask] ≈ pzz[2:length(freqs)+1] + + # Test against in-place. Full precision: + config = MTConfig{Complex{Float64}}(length(z); fs=fs, nw=nw, nfft=nfft) + out = allocate_output(config) + @test eltype(out) == Float64 + + result2 = mt_pgram!(out, z, config) + @test freq(result2) == freq(result) + @test power(result2) ≈ power(result) + + # Lower precision output: + config = MTConfig{Complex{Float32}}(length(z); fs=fs, nw=nw, nfft=nfft) + out = allocate_output(config) + @test eltype(out) == Float32 + + result2 = mt_pgram!(out, z, config) + @test freq(result2) == freq(result) + @test power(result2) ≈ power(result) + + # Lower precision computation: + result3 = mt_pgram!(out, Complex{Float32}.(z), config) + @test freq(result3) == freq(result) + @test power(result3) ≈ power(result) + end diff --git a/test/runtests.jl b/test/runtests.jl index d418e2750..a4a0460e0 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,10 +1,10 @@ -using DSP, FFTW, Test - +using DSP, FFTW, Test +using DSP: allocate_output using Random: seed! -testfiles = [ "dsp.jl", "util.jl", "windows.jl", "filter_conversion.jl", +testfiles = ["dsp.jl", "util.jl", "windows.jl", "filter_conversion.jl", "filter_design.jl", "filter_response.jl", "filt.jl", "filt_stream.jl", - "periodograms.jl", "resample.jl", "lpc.jl", "estimation.jl", "unwrap.jl", + "periodograms.jl", "multitaper.jl", "resample.jl", "lpc.jl", "estimation.jl", "unwrap.jl", "remez_fir.jl" ] seed!(1776) diff --git a/test/util.jl b/test/util.jl index 73af99f72..b302a2744 100644 --- a/test/util.jl +++ b/test/util.jl @@ -90,7 +90,23 @@ end @test shiftin!([1,2,3,4],[5,6]) ≈ [3,4,5,6] ## arraysplit -@test collect(DSP.arraysplit(collect(1:10), 3, 1)) == [ collect(1.0:3), collect(3.0:5), collect(5.0:7), collect(7.0:9)] + +# utility for checking our definition off `size` for `arraysplit` matches how many times we can iterate it +function _length(itr) + c = 0 + for x in itr + c += 1 + end + return c +end + +@testset "`arraysplit`" begin + @test collect(DSP.arraysplit(collect(1:10), 3, 1)) == [ collect(1.0:3), collect(3.0:5), collect(5.0:7), collect(7.0:9)] + + @testset "`arraysplit` with `n_samples`=$(n_samples), `n_samples_per_window`=$(n_samples_per_window), `n_overlap`=$(n_overlap) " for n_samples in (20:20:100), n_samples_per_window in (20:20:100), n_overlap in (0:20:(n_samples_per_window-1)) + @test _length(arraysplit(1:n_samples, n_samples_per_window, n_overlap)) == length(arraysplit(1:n_samples, n_samples_per_window, n_overlap)) + end +end # DELAY FINDING UTILITIES