FIR, or Finite-duration Impulse Response, filters have the distinctive trait that their impulse response lasts for a finite duration of time as opposed to IIR, or Infinite-duration Impulse Response, filters whose impulse response is infinite in duration. This trait is due to the fact that there are no feedback paths in the filter. All Z transform terms are in the numerator. Z transforms written in the Z^-1 notation only contain a "1" in the denominator. Z transforms written in the Z^+1 notation, only have a Z^N in the denominator, where N is the number of states in the filter.
FIR filters offer several advantages over IIR filters:
FIR filters also come with some disadvantages as well:
In practice (e.g., a commercial product called Filter Solutions), you can have at most 1000 taps to create your FIR filter.
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FIR Window Filters
The FIR filters Rectangular, Bartlett, Hanning, Hamming, Blackman, Kaiser, and Dolph-Chebyshev are all Window FIR filters. The name "Window" comes from the fact that these filters are created by scaling a truncated sinc (SIN(X)/X) pattern in time domain with a window to produce the desired frequency effect. Since the ideal frequency response is in a square shape, whose time response is a sinc function and is physically unrealizable, we truncate the sinc function in time domain so as to make it realizable.
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