analytic_wavelet

A translation of J.M. Lilly's code for ridge and element analysis using generalized Morse wavelets into python.

The original jLab repository can be found here: https://github.com/jonathanlilly/jLab

Lilly, J. M. (2019), jLab: A data analysis package for Matlab, v. 1.6.6, http://www.jmlilly.net/jmlsoft.html.

Note that this repository does not re-implement all of the code in jLab, only the parts that I was interested in. It is also not a straight port. I have restructured the code to make the APIs more descriptive and to be more python / numpy friendly. I have also replaced custom functions with built-in numpy and scipy functions where it was obvious to me that I could and I have changed the memory layout to be more efficient in Python (since numpy is row-major and MATLAB is column-major). That means the time axis is usually the last axis in my code but the first axis in jLab. Further simplifications to use more built-in numpy and scipy code can probably be done.

Rough mappings from functions in jLab to functions/methods in analytic_wavelet. Not all APIs map exactly

jLab	analytic_wavelet
anatrans	analytic_transform
instmom	amplitude instantaneous_frequency instantaneous_curvature instantaneous_moments
isomax	ElementAnalysisMorse.isolated_maxima
lininterp	linear_interpolate
maxprops	ElementAnalysisMorse.event_parameters
morseafun	GeneralizedMorseWavelet.amplitude
morsebox	GeneralizedMorseWavelet.heisenberg_box
morsefreq	GeneralizedMorseWavelet.peak_frequency GeneralizedMorseWavelet.energy_frequency GeneralizedMorseWavelet.instantaneous_frequency GeneralizedMorseWavelet.curvature_instantaneous_frequency
morsemom	GeneralizedMorseWavelet.frequency_domain_moment GeneralizedMorseWavelet.energy_moment GeneralizedMorseWavelet.frequency_domain_cumulants GeneralizedMorseWavelet.energy_cumulants
morseprops	GeneralizedMorseWavelet.time_domain_width GeneralizedMorseWavelet.demodulated_skewness_imag GeneralizedMorseWavelet.demodulated_kurtosis
morseregion	ElementAnalysisMorse.region_of_influence (localization region part of morseregion not implemented)
morsespace	GeneralizedMorseWavelet.log_spaced_frequencies
morsewave	GeneralizedMorseWavelet.make_wavelet
morsexpand	GeneralizedMorseWavelet.taylor_expansion_time_domain_wavelet
periodindex	period_indices
quadinterp	quadratic_interpolate
ridgewalk	ridges
ridgemap	RidgeResult.ridge_values RidgeResult.instantaneous_frequency RidgeResult.instantaneous_bandwidth RidgeResult.instantaneous_curvature RidgeResult.total_error RidgeResult.get_values RidgeResult.ridge_ids RidgeResult.collapse
rot	rotate
transmax	maxima_of_transform
transmaxdist	GeneralizedMorseWavelet.distribution_of_maxima_of_transformed_noise
wavespecplot	wavelet_contourf time_series_plot
wavetrans	analytic_wavelet_transform to_frequency_domain_wavelet masked_detrend make_unpad_slices unpad