Filters

In the signal processing jargon a filter is system that takes an input signal and produces an output signal. In this chapter we restrict ourselves to LTI filters 1.

In this section we first look at filters for discrete time signals: the digital filters. This in contrast to analog filters that work on continuous time signals. Most filters nowadays are implemented digitally and work on discrete time signals with a notable exception of filters for audio signals and very high frequency radio signals.

Todo

Rewrite of Filters chapter. Start with the basic types of filters.

Also include the block diagram description (bi-quad)

Footnotes

1

The notion of a filter is not uniquely defined in mathematics. Some applied branches of mathematics define a filter as an idempotent transformation on data. Idempotency is the mathematical notion that expresses that a filter after being applied once does not change the input anymore upon subsequent use. Think of a coffee filter for instance.