Source code for neurokit2.complexity.entropy_spectral

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from ..signal.signal_psd import signal_psd
from .entropy_shannon import entropy_shannon

[docs] def entropy_spectral(signal, bins=None, show=False, **kwargs): """**Spectral Entropy (SpEn)** Spectral entropy (SE or SpEn) treats the signal's normalized power spectrum density (PSD) in the frequency domain as a probability distribution, and calculates the Shannon entropy of it. .. math:: H(x, sf) = -\\sum P(f) \\log_2[P(f)] A signal with a single frequency component (i.e., pure sinusoid) produces the smallest entropy. On the other hand, a signal with all frequency components of equal power value (white noise) produces the greatest entropy. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. bins : int If an integer is passed, will cut the PSD into a number of bins of frequency. show : bool Display the power spectrum. **kwargs : optional Keyword arguments to be passed to ``signal_psd()``. Returns ------- SpEn : float Spectral Entropy info : dict A dictionary containing additional information regarding the parameters used. See Also -------- entropy_shannon, entropy_wiener, .signal_psd Examples ---------- .. ipython:: python import neurokit2 as nk # Simulate a Signal with Laplace Noise signal = nk.signal_simulate(duration=2, sampling_rate=200, frequency=[5, 6, 10], noise=0.1) # Compute Spectral Entropy @savefig p_entropy_spectral1.png scale=100% SpEn, info = nk.entropy_spectral(signal, show=True) @suppress plt.close() .. ipython:: python SpEn Bin the frequency spectrum. .. ipython:: python @savefig p_entropy_spectral2.png scale=100% SpEn, info = nk.entropy_spectral(signal, bins=10, show=True) @suppress plt.close() References ---------- * Crepeau, J. C., & Isaacson, L. K. (1991). Spectral Entropy Measurements of Coherent Structures in an Evolving Shear Layer. Journal of Non-Equilibrium Thermodynamics, 16(2). doi:10.1515/jnet.1991.16.2.137 """ # Sanity checks if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1: raise ValueError( "Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet." ) # Power-spectrum density (PSD) (actual sampling rate does not matter) psd = signal_psd(signal, sampling_rate=1000, **kwargs) # Cut into bins if isinstance(bins, int): psd = psd.groupby(pd.cut(psd["Frequency"], bins=bins), observed=False).agg( "sum" ) idx = psd.index.values.astype(str) else: idx = psd["Frequency"].values # Area under normalized spectrum should sum to 1 (np.sum(psd["Power"])) psd["Power"] = psd["Power"] / psd["Power"].sum() if show is True:, psd["Power"]) if not np.issubdtype(idx.dtype, np.floating): plt.xticks(rotation=90) plt.title("Normalized Power Spectrum") plt.xlabel("Frequency (Hz)") plt.ylabel("Normalized Power") # Compute Shannon entropy se, _ = entropy_shannon(freq=psd["Power"].values) # Normalize se /= np.log2(len(psd)) # between 0 and 1 return se, {"PSD": psd}