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Finite impulse response
A finite impulse response (FIR) filter is a type of a digital filter, that is normally implemented through digital electronic computation. The Z-transform of an FIR filter has only zeros and no poles. The number of coefficients in an FIR filter is its order (sometimes referred to as "taps").
The z-transform of h(n), denoted H(z) is defined as follows:
The z-transform of y(n) is then Y(z) = H(z)X(z).
A FIR filter has a number of useful properties which sometimes make it preferable to an infinite impulse response filter:
- FIR filters are inherently stable
- Require no feedback
- Can have linear phase
An FIR filter has linear phase if and only if its coefficients are symmetric about the center coefficient.
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