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.

.. toctree::

   FIRfilters
   IIRfilters