higher-spectrum 0.2.0

Higher Order Spectral Analysis toolkit

Higher Order Spectral Analysis Toolkit

This package provides a comprehensive set of tools for higher-order spectral analysis in Python. It includes functions for estimating bicoherence, bispectrum, and various orders of cumulants.

Installation

You can install the HOSA toolkit using pip:

pip install higher-spectrum

Contents

Bicoherence

from spectrum import bicoherence, plot_bicoherence

bic, waxis = bicoherence(y, nfft=None, window=None, nsamp=None, overlap=None)
plot_bicoherence(bic, waxis)

Cross Bicoherence

from spectrum import bicoherencex, plot_cross_bicoherence

bic, waxis = bicoherencex(w, x, y, nfft=None, window=None, nsamp=None, overlap=None)
plot_cross_bicoherence(bic, waxis)

Bispectrum Direct (using FFT)

from spectrum import bispectrumd, plot_bispectrum

Bspec, waxis = bispectrumd(y, nfft=None, window=None, nsamp=None, overlap=None)
plot_bispectrum(Bspec, waxis)

Bispectrum Indirect

from spectrum import bispectrumi, plot_bispectrum_indirect

Bspec, waxis = bispectrumi(y, nlag=None, nsamp=None, overlap=None, flag='biased', nfft=None, wind='parzen')
plot_bispectrum_indirect(Bspec, waxis)

Cross Bispectrum (Direct)

from spectrum import bispectrumdx, plot_cross_bispectrum

Bspec, waxis = bispectrumdx(x, y, z, nfft=None, window=None, nsamp=None, overlap=None)
plot_cross_bispectrum(Bspec, waxis)

Cumulants (2nd, 3rd, and 4th order)

from spectrum import cumest, plot_cumulant

order = 2  # 2nd order
y_cum = cumest(y, norder=order, maxlag=20, nsamp=None, overlap=0, flag='biased', k1=0, k2=0)
plot_cumulant(np.arange(-20, 21), y_cum, order)

Cross-Cumulants (2nd, 3rd, and 4th order)

from spectrum import cum2x, cum3x, cum4x, plot_cross_covariance, plot_third_order_cross_cumulant, plot_fourth_order_cross_cumulant

# 2nd order cross-cumulant
ccov = cum2x(x, y, maxlag=20, nsamp=None, overlap=0, flag='biased')
plot_cross_covariance(np.arange(-20, 21), ccov)

# 3rd order cross-cumulant
c3 = cum3x(x, y, z, maxlag=20, nsamp=None, overlap=0, flag='biased', k1=0)
plot_third_order_cross_cumulant(np.arange(-20, 21), c3, k1=0)

# 4th order cross-cumulant
c4 = cum4x(w, x, y, z, maxlag=20, nsamp=None, overlap=0, flag='biased', k1=0, k2=0)
plot_fourth_order_cross_cumulant(np.arange(-20, 21), c4, k1=0, k2=0)

Features

• Estimation of bicoherence and cross-bicoherence
• Direct and indirect methods for bispectrum estimation
• Cross-bispectrum estimation
• Cumulant estimation up to 4th order
• Cross-cumulant estimation up to 4th order
• Plotting functions for all estimations

Requirements

• Python 3.6+
• NumPy
• SciPy
• Matplotlib

Contributing

Contributions to the HOSA toolkit are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License.

Acknowledgements

This toolkit is based on the Higher Order Spectral Analysis toolkit for MATLAB. We've adapted and extended it for Python users.