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Is it possible to replace an FIR with an IIR filter?

Started by Oliver Faust January 21, 2006
Dear group,
I'm new here. I subscribed to comp.dsp because I'm puzzled by a
statement from Simon Haykin in his book:
Adaptive Filter Theory
(fourth edition)

In section 1.6 page 52 he describes the Wold decomposition. There he
writes:

"... A solution of particular interest is an all-zero filter that is
minimum phase, which means that all the zeros of the polynomial B(z)
lie inside the unit circle. In such a case, we may replace the all-zero
filter with an equivalent all-pole filter that has the same impulse
response. ..."

I understand that the all-zero filter refers to an FIR filter and
all-pole refers to an IIR filter. That means the text implies that it
is possible to replace an FIR filter of minimum phase with an
equivalent IIR filter. I always thought this would be impossible.
Any suggestions on that topic?

Greetings,
Oliver Faust

Oliver Faust <oliver.faustremoveme@googlemail.com> wrote:
> I understand that the all-zero filter refers to an FIR filter and > all-pole refers to an IIR filter. That means the text implies that it > is possible to replace an FIR filter of minimum phase with an > equivalent IIR filter.
... but order that IIR will be infinite. The same in case finite IIR -> infinite order FIR.
> I always thought this would be impossible. > Any suggestions on that topic?
Thank you, 
I agree to that.