View source for Finite Impulse Response Filter

'''Finite impulse response''' ('''FIR''') '''filters''' are digital filters carried out by convolution.

[[Image:Fir.png|frame|none|Figure: Impulse response h(n) of a digital filter and [[frequency]] response of the digital filter ([[lowpass|lowpass filter]]).]]


The most straightforward way to implement a digital filter is by convolving the input signal with the digital filter's impulse response (Impulse here in digital signal processing means a pulse with a single nonzero sample). Digital filter's Impulse response is also called a filter kernel.

To implement the fir filter, an input signal x(n) is convolved with fir filter's impulse response h(n), resulting in a filtered output signal y(n). The output signal from a linear system (from our fir filter) is equal to the input signal convolved with the filter's impulse response. the operation (x)*(h) is called convolution.

Convolution is a formal mathematical operation in signal processing: <math>x(n)*h(n)=(n)</math> although the star does not imply multiplication, instead it implies the convolution process. The resulting filtered signal's [[frequency]] response (frequency response of y(n)) follows the shape of filter's frequency response (figure above).

When a filter is implemented by convolution, each sample in the output is calculated by weighting the samples in the input, and adding them together. Recursive filters (iir; infinite impulse response) are an extension of this, using previously calculated values from the output, besides points from the input.

== See also ==
* [[Infinite Impulse Response Filter]] (IIR filter)

[[Category:Signal Processing]]