Re: All Pole representation of LPC

On May 6, 8:35 pm, Olivier Galibert <galib...@xxxxxxxxx> wrote:
On 2009-05-06, farzane.ahm...@xxxxxxxxx <farzane.ahm...@xxxxxxxxx> wrote:

Thank you for your prompt reply
I tried to use your idea and extend the proof to EVERY  ZERO.

I have uploaded my proof as a pdf file here:
http://sites.google.com/site/farzaneahmadi/

Is this proof valid to claim that  "any zero" of a fractional transfer
function -inside or outside the
unit circle- can be approximated as closely as desired by multiple
poles." ?

That's only if you accept the time delay or can read the future.  The
bottom of your transfer function has positive powers of z, which means
looking into the future, instead of negative ones.  So either you have
a non-causal filter which needs to be able to see 'n' samples in the
future, with n increasing with your approximation precision, or you
time-shift everything and end up with a time delay of n samples.

And, btw, your a.z-1 multiplier is a zero at the origin.

  OG.

That was an interesting point. :)
Thank you so much
.

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