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It is easy to classify completely all first-order FIR filters:
where we have normalized
to 1 for simplicity. We have a single
zero at
. If
, the filter is minimum phase. If
, it is maximum phase. Note that the minimum-phase case
is the one in which the impulse response
decays instead of grows. It can be shown that this is a general
property of minimum-phase sequences, as elaborated in the next
section.
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