Digital Filters

A digital LTI filter (or system) takes a signal \(x[n]\) as input and produces output signal \(y[n]\) being the convolution of \(x[n]\) and \(h[n]\), the impulse response of the filter.

In the subsection on FIR filters we discuss the LTI filters with an impulse response \(h[n]\) that is non zero on a bounded subset of \(\setZ\). The filters are called Finite Impulse Response filters.

In the second subsection we look at IIR, Infinite Impulse Response filters. These LTI filters are based on difference equations and can realize filters with infinitely long impulse responses while only using the value of a few samples in the past. This makes them very fast indeed. Unfortunately not all digital filters can be written and implemented as a IIR filter.