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# Discussion Groups | Comp.DSP | Pole zero plot from impulse response

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# Pole zero plot from impulse response - jungledmnc - 2012-10-07 14:18:00

```Please forgive me if this is a dumb question - how can I easily view poles
& zeroes of a filter from its impulse response. I'm trying to analyse some
filter, but all I can get easily is it's impulse response. Pole/zero plot
may really help me understand what's going on in there.

jungledmnc
```
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# Re: Pole zero plot from impulse response - Vladimir Vassilevsky - 2012-10-07 16:43:00

```"jungledmnc" <34728@dsprelated> wrote:

> Please forgive me if this is a dumb question - how can I easily view poles
> & zeroes of a filter from its impulse response.

Unless you know in advance what type of filter function is this, there is no
easy way.

> I'm trying to analyse some
> filter, but all I can get easily is it's impulse response. Pole/zero plot
> may really help me understand what's going on in there.

You have to approximate H(s) or H(z) from the impulse response; and then
solve for poles/zeroes. This is what they call "system identification
problem" and there are tons of books and zillions of methods, depending on
what and how.

DSP and Mixed Signal Consultant
www.abvolt.com

```
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# Re: Pole zero plot from impulse response - Benoit Leprettre - 2012-10-09 07:46:00

```> , but all I can get easily is it's impulse response. Pole/zero plot
> may really help me understand what's going on in there.

Hi,

If all you can get is a recording of the impulse response, you can only try to identify an
"equivalent" filter. That is, a filter that behaves like the one under test, but is
not necessariyl the same.

For example, the actual filter can be of IIR type, but it's transfer function can nevertheless
be fitted with that of a (probably longer) FIR filter. Which is the "right" one?

Therefore, you can hope to identify the _actual_ filter ONLY if you know it's structure : IIR
vs. FIR, number of zeros and poles.

As Vladimir wrote, this a "system identification" problem : I have an input signal, an
output signal, a model structure : let's find the model parameters. Look for "system
identification" and thou shall find your Grail! ;o)
```
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# Re: Pole zero plot from impulse response - Vladimir Vassilevsky - 2012-10-09 09:35:00

```"Benoit Leprettre" <b...@wanadoo.fr> wrote:

> If all you can get is a recording of the impulse response, you can only
> try to identify an "equivalent" filter.
> For example, the actual filter can be of IIR type, but it's transfer
> function can nevertheless be fitted with that of a (probably longer) > FIR
> filter. Which is the "right" one?
>
> Therefore, you can hope to identify the _actual_ filter ONLY if you know
> it's structure : IIR vs. FIR, number of zeros and poles.

Well, if the impulse response is known exactly, then solving a system of
equations once is all that needed to find minimal filter function without
prior assumptions. This is just for academic exercise; any practical method
would involve some kind of curve fit either in frequency or time domain.

DSP and Mixed Signal Consultant
www.abvolt.com

```
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