pybic.BicAn.InstDiffFreq
- BicAn.InstDiffFreq(j, k, fband=0, fwindow=0, dist='gauss', plot=True, err=False, histo=False)[source]
Plot the instantaneous difference frequency vs normalized bispectral modulus.
Here we define
\[\Delta f_{\rm inst}(t) \equiv \frac{1}{2\pi}\frac{d\beta(t)}{dt},\]where, for a single value in bifrequency space \((f_1,f_2)\), the local bispectrum \(\widetilde{\mathcal{B}}\) is given by
\[\widetilde{\mathcal{B}}(t) = X(t,f_1)X(t,f_2)X^*(t,f_1+f_2) = |\widetilde{\mathcal{B}}(t)| e^{i \beta(t)},\]where \(X(t,f)\) is a time-frequency representation. The biphase \(\beta(t)\) is then
\[\beta(t) = \varphi(t,f_1) + \varphi(t,f_2) - \varphi(t,f_1+f_2),\]defining the phases \(\varphi(t,f)\) via \(X(t,f) = |X(t,f)|e^{i\varphi(t,f)}\).
- Parameters:
j (int) – Index 1.
k (int) – Index 2.
fband (float) – Instantaneous frequency bandwidth. Presently affects only the output distribution!
fwindow (float) – Limits for x (frequency) axis.
dist (str) – Choose Gaussian (
'gauss') or Lorentzian distribution.plot (bool) – Plot inst diff freq vs. time.
err (bool) – Plot errorbars instead of timeline.
histo (bool) – Plot phase histogram.
- Returns:
freq, amp, freq_err, um = InstDiffFreq(...)- Return type: