Digital filter

File:FIR.png

In electronics, a digital filter is an electronic filter (usually linear), in discrete time, that is implemented through digital electronic computation. The form of a typical linear digital filter, expressed as a transform in the z-domain, is,

$H(z)={B(z) \over A(z)}={{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}...+b_{M}z^{-M}} \over {1+a_{1}z^{-1}+a_{2}z^{-2}...+a_{M}z^{-M}}}$

where M is the order of the filter.

Note: The parameters of digital filters are generally more stable than the parameters of analog (continuous) filters, primarily because the components of electronic filter change behaviour with temperature. Digital filters can be applied as optimal estimators. Digital filters are either finite impulse response (FIR) or infinite impulse response (IIR), though there is a third hybrid class of filters known as truncated infinite impulse response (TIIR) filters, which show finite impulse responses despite being made from IIR components.

Source: from Federal Standard 1037C and from MIL-STD-188

See also: Butterworth filter, Chebyshev filter, Lowpass filter, Filter design

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