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
All-Pass filter
Started by ●April 1, 2007
Reply by ●April 2, 20072007-04-02
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
Reply by ●April 2, 20072007-04-02
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, > AndorThat's unstable. F.
Reply by ●April 2, 20072007-04-02
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