Re: finding input, given the output of a non-minimum phase system

On Mar 13, 11:38 am, Andor <andor.bari...@xxxxxxxxx> wrote:
Jitesh wrote:
If i have a non minimum phase system and i know it's output at all instants
of time (ie the output is clearly defined), then can i get back the
original input from the knowledge of the given output and the system
transfer function?

in my opinion, yes, in principle. there are practical issues like:

If you have additive measurement noise and a system with a zero in the
frequency response, simple inverse filtering of the output to get the
input will be instable and blow up because of the measurement noise.

this is an issue of definition, because i am not sure i would call a
system "minimum phase" if there *are* zeros lying directly on the unit
circle. just as i am not sure i would call a system "stable" if there
were poles lying directly on the unit circle. but we all agree that
systems with all poles and zeros lying strictly *inside* the unit
circle are stable and minimum phase.

The minimum-phasedness of the system is really irrelevant in this
context -

well, as a practical consideration, i would say the minimum-phasedness
of the system is not *sufficient* to do this, but it is still
*necessary*, solely because of the theoretical reasons. that doesn't
make it irrelevant. just not enough.

any minimum-phase lowpass filter can be a bitch to invert
for a highpass input signal.

well, evaluating a filter with a signal that is perfectly *un*matched
to it, is not a good idea. in fact to evaluate a filter, that it
filters out what it is meant to and passes what it is meant to,
usually requires a reasonably broadband input. doesn't have to be
flat (like white noise), but should be broadbanded.

However, linear-phase systems typically
(but not necessarily) have lots of zeros in the frequency response -

and a good portion of zeros *outside* the unit circle. that's the
killer. the zeros inside don't hurt you.

r b-j



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