pybic.ApplyCWT

pybic.ApplyCWT(sig, samprate=1.0, sigma=3.14, limFreq=2, alphaExp=0.5)[source]

Calculate continuous wavelet transform (CWT) of time-series.

Here we define

CWT[j,k] = A_sigma k^{alphaExp-0.5} sum_{p=0}^{N-1} X[p]

            * exp[ - 2pi^2 (sigma^2 / k^2) (p-k)^2 + 2pi i j p / N  ]

with A_sigma = pi^{1/4} sqrt{2N sigma / samprate} and X is the FFT of x[n].
Parameters:

  • sig (ndarray) – Time series to be analyzed.

  • samprate (float) – Sampling rate.

  • sigma (float) – Time-frequency adjustment.

  • limFreq (int) – Frequency limit division.

  • alphaExp (float) – Alpha exponent.

Returns:

CWT,acwt,freq_vec,time_vec = ApplyCWT(...)

  • CWT (ndarray) - CWT (w/ shape (len(sig)/limFreq, len(sig)/2, Nseries)).

  • acwt (ndarray) - Power spectrum (w/ length len(sig)/limFreq).

  • freq_vec (ndarray) - Frequency vector (w/ length len(sig)/limFreq).

  • time_vec (ndarray) - Time vector (w/ length len(sig)/2).

Return type:

list