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It has been described to me that the wavelet and scaling functions can be computed using the Cascade Algorithm applied to the low and high pass filter coefficients.

Where can I find some proofs of how this happens?

Veak
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Some sources that may be useful include:

  1. "Wavelets and Subband Coding" by Martin Vetterli and Jelena Kovacevic, which provides a comprehensive introduction to wavelets and subband coding, including the derivation of wavelet and scaling functions using the Cascade Algorithm.

  2. "A Wavelet Tour of Signal Processing" by Stephane Mallat, which also provides a detailed introduction to wavelets and subband coding, and includes a proof of how the wavelet and scaling functions can be computed using the Cascade Algorithm.

    Research papers on wavelet transforms and subband coding, which can be found through academic databases such as the IEEE Xplore Digital Library or the ACM Digital Library, many of them will provide detailed proofs of the theory behind the wavelet and scaling functions computation.

ismuta
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  • Having hundreds of pages, would you be so kind to highlight the relevant sections and pages. – Veak Jan 25 '23 at 23:35
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    See https://scicomp.stackexchange.com/questions/42343/numerical-evaluation-of-fourier-transform-of-a-scaling-function/42421#42421 for a start on a faster converging cascade algorithm. My dissertation thesis has the general case, but that is too long for an SE answer. – Lutz Lehmann Jan 29 '23 at 20:43