FPGA Central

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

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?
>
> VLV

What 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.

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?
>
> VLV

Positive 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

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

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

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

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 happening
It is 'noise' caused by the quantizing non-linearities caused by the
AtoD converter.

> and what to
> do with them
Get 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.
>
> VLV
I 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