The Living Thing / Notebooks :

Filter design, linear

especially digital

Linear Time-Invariant (LTI) filter design is a field of signal processing, and a special case of state filtering that doesn’t necessarily involve a hidden state.

z-Transforms, bilinear transforms, Bode plots, design etc.

I am going to consider this in discrete time (i.e. for digital implementation) unless otherwise stated, because I’m implementing this in software, not with capacitors or whatever. For reasons of tradition we usually start from continuous time systems, but this is not necessarily a convenient mathematical or practical starting point for my own work.

This notebook is about designing properties of systems to given specifications, e.g. signal to noise ratios, uncertainty principles…

For inference of filter parameters from data, you want system identification; and for working out the hidden states of the system given the parameters, you want the more general estimation theory in state filters.

Related, musical: delays and reverbs.

Relationship of discrete LTI to continuous time processes

TBD, based on the modern summary in Mart99. But I’m way more interested in representations of systems more naturally represented with delays, and those are easier in digital discrete time than RCL circuit design, so I can’t imagine racing to get to this.

Quick and dirty digital filter design

State-Variable Filters

A vacuous name; every recursive filter has state variables. Less ambiguous: Chamberlin and Zölzer filters.

Nigel Redmon, digital SVF intro.

Refs