FIR transfer function: Difference between revisions

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{{Cleanup rewrite|it is written like a tutorial|FIR transfer function|date=December 2020}}[[Filter (signal processing)#The transfer function|Transfer function filter]] utilizes the transfer function and the [[Convolution theorem]] to produce a filter. In this article, an example of such a filter using finite impulse response is discussed and an application of the filter into real world data is shown.

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== FIR (Finite Impulse Response) Linear filters ==

In digital signal processing, an [[Finite impulse response|FIR filter]] is a time-continuous filter that is invariant with time. This means that the filter does not depend on the specific point of time, but rather depends on the time duration. The specification of this filter uses a [[Linear filter#FIR transfer functions|transfer function]] which hashaving a frequency response whichthat will only pass the desired frequencies of the input. This type of filter is non-recursive, which means that the output can be completely derived at from a combination of the input without any recursive values of the output. This means that there is no feedback loop that feeds the new output the values of previous outputs. This is an advantage over recursive filters such as [[Infinite impulse response|IIR filter (Infinite Impulse Response)]] in the applications that require a linear phase response because it will pass the input without a phase distortion.<ref>IIR Filters and FIR Filters. (2012, June). Retrieved May 04, 2017, from http://zone.ni.com/reference/en-XX/help/370858K-01/genmaths/genmaths/calc_filterfir_iir/</ref>

== Mathematical model ==

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:<math>h(t) = \begin{cases} 0, & \forall &-\infty &\le & t &\le 0 \\ e^{-t}, \quad & \forall &0 &\le & t &\le +\infty \end{cases}</math>

Examine this filter in itsThe frequency ___domain,response we see thatof this frequency responsefilter resembles a [Low-pass filter|[low-pass filter]] as in the lower frequency, the magnitude is being passed and the higher frequency, the magnitude of the filter is being deleted which means that the higher frequency is not transferred.

[[File:Single sided filter frequency response.jpg|Single sided filter frequency response]]