How to derive CWT inverse equation from "Nonorthogonal wavelet transformation for reconstructing gravitational wave signals"

Question

Can someone assist with a complete prove of equation 11, given in the paper (https://arxiv.org/abs/2201.01526) ?

It is a method used for performing inverse fourier transform (or signal reconstruction), following Torrence and Compo's paper on Wavelet analysis(https://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf).

The truth is that, I am unable to reproduce the same equation.

Any assistance/suggestions will be gratefully received.

Thanks in advance!

Answer 1

This is the one-integral inverse. The constants write differently per differences in derivation, but are directly related.