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 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

Acknowledgements

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