F. wrote:
> Andor wrote:

> > W.K. wrote:
> > > If I have a digital all-pass transfer function (IIR)  and I divide out
> > > the numerator/Denominator - is there a theorem somewhere which says
> > > that the 'infinite' polynomial I get has few higher order coefficients
> > > that are significant? ie the higher order terms tend towards zero..??
> > > suppose I have
>
> > > (1-2z^-1)/(1-0.5z^-1) for instance or a second-order example..
>
> > Try
>
> > (1-0.5z^-1) / (1-2z^-1)
>
> > for a counter-example.
>
> > Regards,
> > Andor
>
> That's unstable.
>
> F.

Yes.

Your question was: do the impulse response coefficients always decay
towards zero? My answer was: no, it if the all-pass system is
instable.

Regards,
Andor

On Apr 2, 8:41 pm, "Andor" <andor.bari...@gmail.com> wrote:
> W.K. wrote:
> > If I have a digital all-pass transfer function (IIR)  and I divide out
> > the numerator/Denominator - is there a theorem somewhere which says
> > that the 'infinite' polynomial I get has few higher order coefficients
> > that are significant? ie the higher order terms tend towards zero..??
> > suppose I have
>
> > (1-2z^-1)/(1-0.5z^-1) for instance or a second-order example..
>
> Try
>
> (1-0.5z^-1) / (1-2z^-1)
>
> for a counter-example.
>
> Regards,
> Andor

That's unstable.

F.

W.K. wrote:
> If I have a digital all-pass transfer function (IIR)  and I divide out
> the numerator/Denominator - is there a theorem somewhere which says
> that the 'infinite' polynomial I get has few higher order coefficients
> that are significant? ie the higher order terms tend towards zero..??
> suppose I have
>
> (1-2z^-1)/(1-0.5z^-1) for instance or a second-order example..

Try

(1-0.5z^-1) / (1-2z^-1)

for a counter-example.

Regards,
Andor

If I have a digital all-pass transfer function (IIR)  and I divide out
the numerator/Denominator - is there a theorem somewhere which says
that the 'infinite' polynomial I get has few higher order coefficients
that are significant? ie the higher order terms tend towards zero..??
suppose I have

(1-2z^-1)/(1-0.5z^-1) for instance or a second-order example..

Thanks

W.K