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The transfer function of a finite impulse response filter (FIR
filter) has only a numerator, that is, only zeros in the transfer
function. There is only feed though of a finite number of
increments in the input. The form of the transfer function for a
FIR is
() = −
=0
The transfer function of an infinite impulse response filter (IIR
filter) has a denominator containing the z variable (at least one
pole) and may or may not have zeros. The denominator of the
transfer function represents feedback in the transfer function.
With feedback, the increments in the input feed through the filter
then feed back to the input, resulting in each increment of the
input having infinite increments to the output. The form of the IIR
transfer function is
() = −
=0
−
=0
The transfer function has poles, so this is a discrete-time,
infinite impulse response filter.
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Slide Number 1
