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IIR (infinite impulse response) is a property of signal processing systems. Systems with that property are known as IIR systems or when dealing with electronic filter systems as IIR filters. They have an impulse response function which is non-zero over an infinite length of time. This is in contrast to finite impulse response filters (FIR) which have fixed-duration impulse responses. The simplest analog IIR filter is an RC filter made up of a single resistor (R) feeding into a node shared with a single capacitor (C). This filter has an exponential impulse response characterized by an RC time constant.

IIR filters may be implemented as either analog or digital filters. In digital IIR filters, the output feedback is immediately apparent in the equations defining the output. Note that unlike with FIR filters, in designing IIR filters it is necessary to carefully consider "time zero" case in which the outputs of the filter have not yet been clearly defined.

Design of digital IIR filters is heavily dependent on that of their analog counterparts which is because there are plenty of resources, works and straightforward design methods concerning analog feedback filter design while there are hardly any for digital IIR filters. As a result, mostly, if a digital IIR filter is going to be implemented, first, an analog filter (e.g. Chebyshev filter, Butterworth filter, Elliptic filter) is designed and then it is converted to digital by applying discretization techniques such as Bilinear transform or Impulse invariance.

In practice, electrical engineers find IIR filters to be fast and cheap, but with poorer bandpass filtering and stability characteristics than FIR filters.

Example IIR filters include the Chebyshev filter, Butterworth filter, and the Bessel filter.

In the following subsections we focus on discrete time IIR filters which can be implemented in Digital Signal Processors.

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