Examples vs Scipy, PyWavelets

[OverLordGoldDragon]

A thread to share/discuss example comparisons between implementations.

[OverLordGoldDragon]

1. Real chirp + distortions. CWT, complex morlet. -- all coefficients L1-normalized. (-- code)

• Low scales: heavy artifacts for scipy, medium for pywt, none for ssqueezepy
• Mid scales: ssqueezepy has least uncertain frequency band; pywt and scipy are even

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• Low scales: rip scipy; excess energy in lower scales, which is why the rest of the plot looks dark.
• Mid scales: moderate contamination near boundaries for pywt, slight for scipy, none for ssqueezepy.
• High scales: ssqueezepy dominating with a low-uncertainty band. pywt and scipy suffering from a vertically wide band.

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• Low scales: pywt and scipy capture amplitude modulation due to aliasing. ssqueezepy is robust to it; whether or not that's desired might differ, but pywt and scipy seem to clearly exaggerate the effects of aliasing.

• Low scales: not very clear here due to x_high, but squeezepy is virtually blind to noise at very low frequencies, whereas pywt and scipy certainly aren't.
• Mid & large scales: all affected pretty much same way

[OverLordGoldDragon]

2. Pure tones; mixed, transitioning -- same plot layout as in 1 (-- code)

• Boundary effects: visible for scipy and pywt, none for ssqueezepy; symmetric padding is advantageous if the extension is of a periodic signal, and differentiable at boundary
• Energy resolution: ssqueezepy captures relative energies more accurately

[OverLordGoldDragon]

ssqueezepy.cwt_fwd higher scales mystery solved; it is a boundary effect due to discontinuous first derivative of sin using symmetric extension; replacing with cos vanishes the effect. This can also be seen with padsignal inserted in pywt.cwt.

[OverLordGoldDragon]

Extensive breakdown.