Skip to main content

Spectral

Namespace: UTILSLIB  ·  Library: Utilities Library  ·  Source: math/spectral.h

#include <utils/spectral.h>

class UTILSLIB::Spectral

Static multi-taper spectral estimator producing tapered spectra, PSDs and cross-spectral density matrices over Eigen row inputs.

Designed for fan-out across channels via QtConcurrent and feeding CONNECTIVITYLIB's coherence / phase estimators.

Static multi-taper spectra, PSD and CSD estimator for MEG/EEG time series.

src/examples/ex_math/main.cpp
const int nSamples = 200;
const double sFreq = 100.0;
RowVectorXd signal(nSamples);
for (int t = 0; t < nSamples; ++t) {
    signal(t) = 2.0 * std::sin(2.0 * kPi * 10.0 * t / sFreq); // 10 Hz, amplitude 2
}
const auto [tapers, weights] = Spectral::generateTapers(nSamples, std::string("hanning"));
const MatrixXcd spectra = Spectral::computeTaperedSpectraRow(signal, tapers, nSamples);
const RowVectorXd psd = Spectral::psdFromTaperedSpectra(spectra, weights, nSamples, sFreq);
const VectorXd freqs = Spectral::calculateFFTFreqs(nSamples, sFreq);

Public Methods​

Spectral()​

deleted default constructor (static class).

Static Methods​

computeTaperedSpectraRow(vecData, matTaper, iNfft)​

Calculates the full tapered spectra of a given input row data.

Parameters:

  • vecData : const Eigen::RowVectorXd & input roww data (time domain), for which the spectrum is computed.

  • matTaper : const Eigen::MatrixXd & tapers used to compute the spectra.

  • iNfft : int FFT length.

Returns:

  • Eigen::MatrixXcd — tapered spectra of the input data.

computeTaperedSpectraMatrix(matData, matTaper, iNfft, bUseThreads)​

Calculates the full tapered spectra of a given input matrix data.

This function calculates each row in parallel.

Parameters:

  • matData : const Eigen::MatrixXd & input matrix data (time domain), for which the spectrum is computed.

  • matTaper : const Eigen::MatrixXd & tapers used to compute the spectra.

  • iNfft : int FFT length.

  • bUseThreads : bool Whether to use multiple threads.

Returns:

  • QVector< Eigen::MatrixXcd > — tapered spectra of the input data.

compute(inputData)​

Computes the tapered spectra for a row vector.

This function gets called in parallel.

Parameters:

Returns:

  • Eigen::MatrixXcd — The tapered spectra for one data row.

reduce(finalData, resultData)​

Reduces the taperedSpectra results to a final result.

This function gets called in parallel.

Parameters:

  • finalData : QVector< Eigen::MatrixXcd > & The final data data.

  • resultData : const Eigen::MatrixXcd & The resulting data from the computation step.

psdFromTaperedSpectra(matTapSpectrum, vecTapWeights, iNfft, dSampFreq)​

Calculates the power spectral density of given tapered spectrum.

Parameters:

  • matTapSpectrum : const Eigen::MatrixXcd & tapered spectrum, for which the PSD is calculated.

  • vecTapWeights : const Eigen::VectorXd & taper weights.

  • iNfft : int FFT length.

  • dSampFreq : double sampling frequency of the input data.

Returns:

  • Eigen::RowVectorXd — power spectral density of a given tapered spectrum.

csdFromTaperedSpectra(vecTapSpectrumSeed, vecTapSpectrumTarget, vecTapWeightsSeed, vecTapWeightsTarget, iNfft, dSampFreq)​

Calculates the cross-spectral density of the tapered spectra of seed and target.

Parameters:

  • vecTapSpectrumSeed : const Eigen::MatrixXcd & tapered spectrum of the seed.

  • vecTapSpectrumTarget : const Eigen::MatrixXcd & tapered spectrum of the target.

  • vecTapWeightsSeed : const Eigen::VectorXd & taper weights of the seed.

  • vecTapWeightsTarget : const Eigen::VectorXd & taper weights of the target.

  • iNfft : int FFT length.

  • dSampFreq : double sampling frequency of the input data.

Returns:

  • Eigen::RowVectorXcd — cross-spectral density of the tapered spectra of seed and target.

calculateFFTFreqs(iNfft, dSampFreq)​

Calculates the FFT frequencies.

Parameters:

  • iNfft : int FFT length.

  • dSampFreq : double sampling frequency of the input data.

Returns:

  • Eigen::VectorXd — FFT frequencies.

generateTapers(iSignalLength, sWindowType)​

Calculates a hanning window of given length.

Parameters:

  • iSignalLength : int length of the hanning window.

  • sWindowType : const QString & type of the window function used to compute tapered spectra.

Returns:

  • QPair< Eigen::MatrixXd, Eigen::VectorXd > — Qpair of tapers and taper weights.

generateTapers(iSignalLength, sWindowType)​

Calculates a hanning window of given length.

Parameters:

  • iSignalLength : int length of the hanning window.

  • sWindowType : const std::string & type of the window function used to compute tapered spectra.

Returns:

  • std::pair< Eigen::MatrixXd, Eigen::VectorXd > — Qpair of tapers and taper weights.

Example​

Used in examples​

ex_spectral​

Multitaper spectra, power spectral density and cross-spectral density of random test signals.

src/examples/ex_spectral/main.cpp, line 80
//Generate hanning window
QPair<MatrixXd, VectorXd> tapers = Spectral::generateTapers(iNSamples, QString("hanning"));
MatrixXd matTaps = tapers.first;
VectorXd vecTapWeights = tapers.second;
int iNfft = iNSamples;

Authors of this file​