Editing Finite impulse response (section)

==Properties==

An FIR filter has a number of useful properties which sometimes make it preferable to an [[infinite impulse response]] (IIR) filter. FIR filters:
*Require no feedback. This means that any rounding errors are not compounded by summed iterations. The same relative error occurs in each calculation. This also makes implementation simpler.
*Are inherently [[BIBO stability|stable]], since the output is a sum of a finite number of finite multiples of the input values, so can be no greater than <math display="inline"> \sum |b_i|</math> times the largest value appearing in the input.
*Can easily be designed to be [[linear phase]] by making the coefficient sequence symmetric. This property is sometimes desired for phase-sensitive applications, for example data communications, [[seismology]], [[Audio crossover|crossover filters]], and [[Audio mastering|mastering]].

The main disadvantage of FIR filters is that considerably more computation power in a general purpose processor is required compared to an IIR filter with similar sharpness or [[selectivity (radio)|selectivity]], especially when low frequency (relative to the sample rate) cutoffs are needed.  However, many digital signal processors provide specialized hardware features to make FIR filters approximately as efficient as IIR for many applications.