# Coefficient quantisation for FIR filters

Started by March 10, 2011
```Hi,

can someone tell me (a hint perhaps) why there is a larger effect on the
filter response after coefficient quantization in IIR filters than FIR
filters.

Several books mention this but do not go on to explain it in detail.

Is it because of the feedback term in IIR filters?

or is the coefficient quantization sensitive to poles than zeros?

```
```
third_person wrote:

> Hi,
>
> can someone tell me (a hint perhaps) why there is a larger effect on the
> filter response after coefficient quantization in IIR filters than FIR
> filters.

Hint: take a partial derivative of H(z) by a coefficient.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
```On Thu, 10 Mar 2011 04:48:57 -0600, third_person wrote:

> Hi,
>
> can someone tell me (a hint perhaps) why there is a larger effect on the
> filter response after coefficient quantization in IIR filters than FIR
> filters.
>
> Several books mention this but do not go on to explain it in detail.
>
> Is it because of the feedback term in IIR filters?
>
> or is the coefficient quantization sensitive to poles than zeros?

If you shift a zero from 0.99 to 1.00 does it have as much effect on the
filter output as if you shift a pole from 0.99 to 1.00?

Mathematics doesn't always yield well to "why" questions -- it does what
it does because that's how the math works out.  But the closest answer, I
think, is because your coefficient quantization will shift poles around,
and moving a pole that's close to the stability boundary has a much
larger effect on settling than moving a zero.

--
http://www.wescottdesign.com
```
```On Mar 10, 11:48&#2013266080;pm, "third_person"
<third_person@n_o_s_p_a_m.ymail.com> wrote:
> Hi,
>
> can someone tell me (a hint perhaps) why there is a larger effect on the
> filter response after coefficient quantization in IIR filters than FIR
> filters.
>
> Several books mention this but do not go on to explain it in detail.
>
> Is it because of the feedback term in IIR filters?
>
> or is the coefficient quantization sensitive to poles than zeros?

Because one has stability to watch and the other does not.
```
```Vlad is correct. If you're in a hurry and don't have time to dust off your partial derivative skills, check out pg. 613-620 of Digital Signal Processing: Principles, Applications, and Algorithms (Fourth Edition - Proakis/ Manolakis). They do a wonderful job, and have great plots that illustrate multiple issues.

Not only is maximum pole separation critical (hence two pole bi-quads are ideal for real calculations - single pole sections are ideal if you can justify the cost of complex calculations), but the actual implementation structure is just as important in determining what possible poles you system can truly take on with quantized coefficients.

It's a great little read I recommend since you seem curious to find out why, and I found it satisfying when I was in your position (all other books stated it as a truism, just mentioning it in passing).

Bryan
```
```On Fri, 11 Mar 2011 18:46:10 -0800 (PST), Bryan <bryan.paul@gmail.com>
wrote:

>Vlad is correct. If you're in a hurry and don't have time to dust off
>your partial derivative skills, check out pg. 613-620 of Digital Signal
>Processing: Principles, Applications, and Algorithms (Fourth Edition - Proakis/ Manolakis).
>They do a wonderful job, and have great plots that illustrate multiple issues.

Hi Bryan,
Can you tell us the The Chapter and Section numbers
for the 4th-Edition material on pages 613-620.

I'm trying to see if that material is also in
Proakis' & Manolakis' 3rd Edition.

Thanks,
[-Rick-]
```
```Sorry Rick! I suppose that would help more people that have the other editions:

Chapter 9: Implementation of Discrete-Time Systems
\ Section 9.5: Quantization of Filter Coefficients
\ \ Subsection 9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients

Bryan
```
```On Sun, 13 Mar 2011 09:53:57 -0700 (PDT), Bryan <bryan.paul@gmail.com>
wrote:

>Sorry Rick! I suppose that would help more people that have the other editions:
>
>Chapter 9: Implementation of Discrete-Time Systems
> \ Section 9.5: Quantization of Filter Coefficients
> \ \ Subsection 9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients
>
>Bryan

Hi Bryan,
Thanks forthe additional information.  In the
Third Edition of the book, the following exists:

Chapter 7: Implementation of Discrete-Time Systems
\ Section 7.6: Quantization of Filter Coefficients
\ \ Subsection 7.6.1 Analysis of Sensitivity to
Quantization of Filter Coefficients

That material starts on page 569 in the Third Edition.

See Ya',
[-Rick-]

```