In
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...
, a recursive filter is a type of
filter which reuses one or more of its outputs as an input. This
feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handle ...
typically results in an unending
impulse response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reac ...
(commonly referred to as ''
infinite impulse response
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) that does not become exactly zero past a certain point but continues indefinitely. This is in ...
'' (IIR)), characterised by either
exponentially growing,
decaying, or
sinusoid
A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is '' simple harmonic motion''; as rotation, it correspond ...
al signal output components.
However, a recursive filter does not always have an infinite impulse response. Some implementations of moving average filter are recursive filters but with a finite impulse response.
Non-recursive Filter Example:
y
= 0.5x
− 1+ 0.5x
Recursive Filter Example:
y
= 0.5y
− 1+ 0.5x
Examples of recursive filters
*
Kalman filter
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...
Signal processing
{{signal-processing-stub