Linear and Nonlinear Digital Filters: From the Analog and Beyond

Abstract

Abstract A common approach in the development of digital filters is to begin with an existing analog filter and produce an equivalent computer program to realize it. This may involve, at the extreme, the detailed analysis of circuit behavior, or it may stem from a higher-level approach that looks at block diagrams and s-domain transfer functions. In this article, we first take the latter approach to develop a set of linear filters from the well-known state variable filter. From this we obtain a first result, which is a linear digital implementation of the Steiner design, comprising separate inputs for different frequency responses and a single output summing the responses. Turning back to the state variable design, we show that to develop a nonlinear version, an analog circuit realization can be used to identify positions in which to insert nonlinear waveshapers. This gives us our second result, a nonlinear digital state variable filter. From this analog-derived design, we then propose modifications that go beyond the original filter, developing as a final result a structure that could be classed as a hybrid of filter and digital waveshaper. As part of this process, we ask the question of whether an approach that takes inspiration from the analog world, while being decoupled from it, may be more profitable in the long run than an obsession with detailed circuit modeling.