All Pole representation of LPC

Hi
I am reffering to the following discussion from:
http://www.dsprelated.com/groups/speechcoding/show/340.php
which states that :

From the book "Digital Processing of Speech Signals" by Rabiner &
Schafer,
We have the following comments:

“we may use the fact that effect of zero of the transfer function can
be achieved by including more poles." (page 99).
As a proof of the above statement, the reader is asked to refer to the
Problem 3.10 on page 112, which I repeat here:

"Show that if |a| < 1,
1-a*z^(-1) = 1/(summation(a^n * z^(-n))), where n goes
from 0 to infinity"

and thus, any zero “inside the unit circle” ( |a| < 1,) can be
approximated as closely as desired by multiple poles."

My question is whether we can extend the proof to the zeros outside
the unit circle also and whether the following statement is valid:

"any zero" of a fractional transfer function -inside or outside the
unit circle- can be approximated as closely as desired by multiple
poles."

I need this for application of lpc method on a general fractional
trandfer function.
.

Relevant Pages

  • Re: Poles an Zeros
    ... Could someone explain to me Poles and Zeros. ... If you know the transfer function, ... the numerator hits zero, and "poles" where the denominator hits zero. ... You estimate the frequency response by pretending that S is the input ...
    (sci.electronics.basics)
  • Re: Minimum-Phase Systems Characteristics
    ... responses don't really have poles or zeros, ... get a real impulse response) and a constant phase response of -45°.. ... phase spectrum is zero. ... Any zero inside the unit circle will cancel out the ...
    (comp.dsp)
  • Re: Poles an Zeros
    ... Basically, you can express the behavior of a linear, continuous-time, time-invariant system with a mathematical construct called a "transfer function". ... It turns out to be very easy to calculate the response of such a system to a continuous sine wave at a particular frequency -- in this case the poles of a system will tend to make the system gain go down as the frequency is increased, and the zeros will make the gain go up. ... Do you need to implement control loops in software? ...
    (sci.electronics.basics)
  • Re: Evolutionist says you cant build a large wooden ship
    ... at least one and absolutely zero of them saying there must be two. ... I think I can see that two poles can be arbitrarily close, but to have them coincide would require that some arbitrarily small area would always contain two tangents at 180 degrees to each other, which I think contradicts the definition of "smooth". ... no indication of how _many_ zero points will be present in vector fields on a sphere. ... _no_ zeros of the tangent field. ...
    (talk.origins)
  • Re: Partial Fraction Decomposition in c++
    ... I have the polynomial of the transfer function including its roots. ... where the poles lie. ... I want to calculate the magnitude of the transfer function at that pole by ...
    (comp.dsp)