Example Allpass Filters
- The simplest allpass filter is a unit-modulus gain
can be any phase value. In the real case
can only be 0 or
, in which case
.
- A lossless FIR filter can consist only of a single nonzero tap:
, where
is again some constant phase, constrained to be 0 or
in the real-filter case. Since we are considering only causal filters here,
. As a special case of this example, a unit delay
is a simple FIR allpass filter.
- The transfer function of every finite-order, causal,
lossless IIR digital filter (recursive allpass filter) can be written as
where,
, and
. The polynomial
can be obtained by reversing the order of the coefficients in
and conjugating them. (The factor
serves to restore negative powers of
and hence causality.)
![$ \,$](http://www.dsprelated.com/josimages_new/pasp/img196.png)
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