Vincent Herrmann (@vidivinci)

Classically trained pianist and composer. Through electronic avant-garde music I came into touch with audio engineering and digital signal processing. Currently I am fascinated by the points of contact between some DSP techniques and deep learning that may lead to undreamt creative tools. vincentherrmann.github.io

Wavelets II - Vanishing Moments and Spectral Factorization

Vincent Herrmann ● October 11, 2016

This post walks through how vanishing moments turn into concrete algebraic constraints on wavelet filter coefficients, and why that leads to Daubechies filters. It explains how a wavelet with A vanishing moments is orthogonal to all polynomials up to degree A minus one, and it shows how those continuous conditions become discrete sums like sum_k k^n h1(k)=0. Expect clear links between approximation power and filter length.

Wavelets I - From Filter Banks to the Dilation Equation

Vincent Herrmann ● September 28, 2016●9 comments

Starting from a practical cascaded FIR filter bank, this post derives the key equations behind the Fast Wavelet Transform. It shows how conjugate-quadrature analysis and synthesis filters give perfect reconstruction and how iterating the cascade produces the scaling function, leading to the dilation equation. DB4 coefficients are used as a concrete example and a linear-system trick yields exact integer-sample values of the scaling function.

No Threads Found