When doing the AR analysis, sometimes the result has the negative stable real poles in Z domain. If we try to map those poles into S domain, they correspond to the complex conjugate pairs with the imm part of +/- Pi, i.e. above Nyquist. What should be the interpretation of this result? VLV

# System Identification

Started by ●July 16, 2008

Reply by ●July 17, 20082008-07-17

On Jul 17, 1:40 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> When doing the AR analysis, sometimes the result has the negative stable > real poles in Z domain. If we try to map those poles into S domain, they > correspond to the complex conjugate pairs with the imm part of +/- Pi, > i.e. above Nyquist. > > What should be the interpretation of this result? > > VLVWhat do you mean negative stable? You mean poles with negative real parts ie stable nbecome unstable. State how you find the z-domain version first and then maybe we can answer. Eg do you use Tustins method? K.

Reply by ●July 17, 20082008-07-17

On 17 Jul., 03:40, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> When doing the AR analysis, sometimes the result has the negative stable > real poles in Z domain. If we try to map those poles into S domain, they > correspond to the complex conjugate pairs with the imm part of +/- Pi, > i.e. above Nyquist. > > What should be the interpretation of this result? > > VLVPositive real poles indicate a DC component multiplied with a decaying exponential. Negative real poles indicate a Nyquist component multiplied with a decaying exponential. Compute the AR coefficients of these two signals: x1[n] = exp(-0.5 n) and x2[n] = exp(-0.5 n) cos(pi n). Regards, Andor

Reply by ●July 17, 20082008-07-17

Andor wrote:> On 17 Jul., 03:40, Vladimir Vassilevsky <antispam_bo...@hotmail.com> > wrote: > >>When doing the AR analysis, sometimes the result has the negative stable >>real poles in Z domain. If we try to map those poles into S domain, they >>correspond to the complex conjugate pairs with the imm part of +/- Pi, >>i.e. above Nyquist. >> >>What should be the interpretation of this result? >>> Positive real poles indicate a DC component multiplied with a decaying > exponential. Negative real poles indicate a Nyquist component > multiplied with a decaying exponential.Dr. Andor is right as usual! I wonder how and why the real negative poles are happening, and what to do with them. The data doesn't seem to suggest anything like decaying exponentials at or near Nyquist. VLV

Reply by ●July 17, 20082008-07-17

On 17 Jul, 19:43, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> I wonder how and why the real negative poles are happening, and what to > do with them. The data doesn't seem to suggest anything like decaying > exponentials at or near Nyquist.Don't know why they appear, but you might try to just ignore them. Factor them out of the AR model and go on with whatever you do, using the remaining poles. Rune

Reply by ●July 17, 20082008-07-17

On Jul 17, 1:43�pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> I wonder how and why the real negative poles are happening, and what to > do with them. The data doesn't seem to suggest anything like decaying > exponentials at or near Nyquist.I do not know whether the mechanism is the same, but I have seen similar behavior in ARMA FDLS when a sine wave input is used instead of a cosine wave. I determined the cause to be the "zero input / non- zero output" situation that occurs when sine waves are sampled at Fs/2 (at the zero-crossings) -- the mathematics respond to this indeterminate case by putting one or more poles near exp(jPI). Depending on exactly what type of AR analysis you're doing, I wonder if there might be some similar sort of mechanism in place. The only AR analysis that I have ever done was with linear predictors and the resultant all-pole transfer functions, but I never encountered this problem there. Greg

Reply by ●July 18, 20082008-07-18

On Jul 17, 10:43�am, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> Andor wrote: > > On 17 Jul., 03:40, Vladimir Vassilevsky <antispam_bo...@hotmail.com> > > wrote: > > >>When doing the AR analysis, sometimes the result has the negative stable > >>real poles in Z domain. If we try to map those poles into S domain, they > >>correspond to the complex conjugate pairs with the imm part of +/- Pi, > >>i.e. above Nyquist. > > >>What should be the interpretation of this result? > > > Positive real poles indicate a DC component multiplied with a decaying > > exponential. Negative real poles indicate a Nyquist component > > multiplied with a decaying exponential. > > Dr. Andor is right as usual! > > I wonder how and why the real negative poles are happeningIt is 'noise' caused by the quantizing non-linearities caused by the AtoD converter.> and what to > do with themGet rid of them by smoothing the data, sampling at a slower rate, using higher resolution AtoD converters or use a better technique to do system identification. I don't know which method you are using now. All the things I mentioned helped but the smooth and sampling a slower data rate didn't work well. Now you know what the problem is the cure is easy to find. Note, the least squares system identification method you see in text books doesn't work well when the data is quantized.> The data doesn't seem to suggest anything like decaying > exponentials at or near Nyquist. > > VLVI believe you. I have seen it before and fought those battles. A couple weeks ago you had a thread on the same topic and there were some methods mentioned there. Did you try them? Peter Nachtwey