CWT: squeezepy vs. pywt

[OverLordGoldDragon]

No description provided.

[OverLordGoldDragon]

• N = len(x) (actually closer power of 2 to len)
• u(a) == j (pywt)
• DIFF = np.diff
• Aside np.diff, coef_a for the two look similar - in fact, may be identical:
  • iFFTshift seems to just move points around, namely swapping two halves of a sequence
  • The swapping may be due to how xi is defined (see plot); if defined monotonically, the shift may be redundant
  • ssqueezepy wavelet is in fact the Fourier transform of the Morlet wavelet, not the wavelet itself
  • Thus, the inside of iFFT may be identical for ssqueezepy and pywt, though it remains uncertain how pywt exactly defines the non-integrated wavelet, or what effect integration has
  • Scaling of the window function w is also different
• np.diff is a discrete-time derivative, off by a scaling factor; maybe that's the purpose of sqrt(a)?
• pywt.coef: why the minus sign?

Further info, and pywt implem. docs

[OverLordGoldDragon]

• periodic, folded, boundary wavelets: pdf
• boundary wavelets code

[OverLordGoldDragon]

Adios, headless chicken.