Editing Linear filter (section)

=== Implementation issues ===

Classical analog filters are IIR filters, and classical filter theory centers on the determination of transfer functions given by low order [[rational functions]], which can be synthesized using the same small number of reactive components.<ref>However, there are a few cases in which FIR filters directly process analog signals, involving non-feedback topologies and analog delay elements. An example is the discrete-time ''[[analog sampled filter]]'', implemented using a so-called [[bucket-brigade device]] clocked at a certain sampling rate, outputting copies of the input signal at different delays that can be combined with some weighting to realize an FIR filter. Electromechanical filters such as [[Electronic filter#SAW filters|SAW filters]] can likewise implement FIR filter responses; these operate in continuous time and can thus be designed for higher frequencies.</ref> Using digital computers, on the other hand, both FIR and IIR filters are straightforward to implement in software.

A digital IIR filter can generally approximate a desired filter response using less computing power than a FIR filter, however this advantage is more often unneeded given the increasing power of digital processors. The ease of designing and characterizing FIR filters makes them preferable to the filter designer (programmer) when ample computing power is available. Another advantage of  FIR filters is that their impulse response can be made symmetric, which implies a response in the frequency domain that has [[linear phase|zero phase at all frequencies]] (not considering a finite delay), which is absolutely impossible with any IIR filter.<ref>Outside of trivial cases, stable IIR filters with zero phase response are possible if they are not causal (and thus are unusable in real-time applications) or implementing transfer functions classified as unstable or "marginally stable" such as a [[double integrator]].</ref>