Editing Linear filter (section)

==Example implementations==

A popular circuit implementing a second order active R-C filter is the [[Sallen Key filter|Sallen-Key]] design, whose schematic diagram is shown here. This topology can be adapted to produce low-pass, band-pass, and high pass filters.

[[File:FIR Filter.svg|thumb|300px|right|A discrete-time FIR filter of order ''N''. The top part is an ''N''-sample delay line; each delay step is denoted ''z''<sup>−1</sup>.]]

An N<sup>th</sup> order FIR filter can be implemented in a discrete time system using a computer program or specialized hardware in which the input signal is subject to N delay stages. The output of the filter is formed as the weighted sum of those delayed signals, as is depicted in the accompanying signal flow diagram. The response of the filter depends on the weighting coefficients denoted ''b<sub>0</sub>'', ''b<sub>1</sub>'', .... ''b<sub>N</sub>''. For instance, if all of the coefficients were equal to unity, a so-called [[boxcar function]], then it would implement a low-pass filter with a low frequency gain of N+1 and a frequency response given by the [[sinc function]]. Superior shapes for the frequency response can be obtained using coefficients derived from a more sophisticated design procedure.