Yes, CWT.vi uses the equation 9-2 in the SPT user manual. CWT is NOT a
form of DWT.

"Continuous" in CWT.vi does not mean online processing signal. CWT.vi
from SPT computes the discretised Dyadic Wavelet Transform for a
discrete signal. You may also refer to page 148 in the book, a Wavelet
Tour of Signal Processing (Stephane Mallat), for more information on
Dyadic Wavelet Transform.

If the analysis filter coefficients are provided, the mother wavelet
is computed with the analysis filter coefficients and then use
equation 9-2 again.

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