kirchner_numba (pyleoclim.utils.wavelet.kirchner_numba)

pyleoclim.utils.wavelet.kirchner_numba(ys, ts, freq, tau, c=0.012665147955292222, Neff=3, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False, nproc=1)[source]

Return the weighted wavelet amplitude (WWA) modified by Kirchner.

Using numba.

Parameters

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) – None - the original time series is assumed to have no trend; ‘linear’ - a linear least-squares fit to ys is subtracted; ‘constant’ - the mean of ys is subtracted ‘savitzy-golay’ - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y. Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

References

Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996). Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12, 345–352 (2005).