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# Discussion Groups | Comp.DSP | Combining multiple CIC decimation filters in series

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# Combining multiple CIC decimation filters in series - SRB - 2012-10-31 09:45:00

```Hi All
I'm designing a CIC filter to be used at high decimation rates (e.g. 4000)
and am considering whether it could be beneficial to use more than CIC
filter in series. For example, rather than having one CIC that decimates by
4000 I could use four CICs that decimate by 10, 10, 10 and 4x
respectively.

I have done some quick calculations that suggest that, if I have 4 CICs
decimating by 10/10/10/4x, with orders of 3/6/6/6 respectively, the number
of operations per input sample is similar to having one CIC with 4000x
decimation and order 4, but the attenuation of power aliased into the
wanted band is much better, so it seems like using multiple CICs could be
advantageous under some circumstances. However I haven't been able to find
scholar.

So my questions are:

1) Do people typically combine multiple CIC filters in series in this way?
and if not, why not?
2) Are there any guidelines or rules of thumb as to how to select the
number of filters to use and what decimation factor to use in each? (e.g.
any publications similar to that of Crochiere and Rabiner 1975 for FIRs)

Thanks very much,
Sharon

```
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# Re: Combining multiple CIC decimation filters in series - Tim Wescott - 2012-10-31 12:21:00

```On Wed, 31 Oct 2012 08:45:09 -0500, SRB wrote:

> Hi All
> I'm designing a CIC filter to be used at high decimation rates (e.g.
> 4000) and am considering whether it could be beneficial to use more than
> CIC filter in series. For example, rather than having one CIC that
> decimates by 4000 I could use four CICs that decimate by 10, 10, 10 and
> 4x respectively.
>
> I have done some quick calculations that suggest that, if I have 4 CICs
> decimating by 10/10/10/4x, with orders of 3/6/6/6 respectively, the
> number of operations per input sample is similar to having one CIC with
> 4000x decimation and order 4, but the attenuation of power aliased into
> the wanted band is much better, so it seems like using multiple CICs
> could be advantageous under some circumstances. However I haven't been
> able to find any mention of people using this approach when searching
>
> So my questions are:
>
> 1) Do people typically combine multiple CIC filters in series in this
> way? and if not, why not?
> 2) Are there any guidelines or rules of thumb as to how to select the
> number of filters to use and what decimation factor to use in each?
> (e.g. any publications similar to that of Crochiere and Rabiner 1975 for
> FIRs)
>
> Any thoughts/opinions/suggestions gratefully received. Thanks very much,
> Sharon

You do know that the first 'C' in CIC stands for "cascaded", yes?

I seem to remember seeing something like this done, but I'm not a Tall
God of signal processing like some of the other's here.  I'm just a
control systems guy, where CIC filters do not prevail.

If the math works out, and the resulting spectrum is what you want,
what's not to like?

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
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# Re: Combining multiple CIC decimation filters in series - SG - 2012-10-31 12:51:00

```Am 31.10.2012 17:21, schrieb Tim Wescott:
> On Wed, 31 Oct 2012 08:45:09 -0500, SRB wrote:
>
>> Hi All
>> I'm designing a CIC filter to be used at high decimation rates (e.g.
>> 4000) and am considering whether it could be beneficial to use more than
>> CIC filter in series. For example, rather than having one CIC that
>> decimates by 4000 I could use four CICs that decimate by 10, 10, 10 and
>> 4x respectively.
>>
>> I have done some quick calculations that suggest that, if I have 4 CICs
>> decimating by 10/10/10/4x, with orders of 3/6/6/6 respectively, the
>> number of operations per input sample is similar to having one CIC with
>> 4000x decimation and order 4, but the attenuation of power aliased into
>> the wanted band is much better, so it seems like using multiple CICs
>> could be advantageous under some circumstances. However I haven't been
>> able to find any mention of people using this approach when searching
>>
>> So my questions are:
>>
>> 1) Do people typically combine multiple CIC filters in series in this
>> way? and if not, why not?
>> 2) Are there any guidelines or rules of thumb as to how to select the
>> number of filters to use and what decimation factor to use in each?
>> (e.g. any publications similar to that of Crochiere and Rabiner 1975 for
>> FIRs)
>>
>> Any thoughts/opinions/suggestions gratefully received. Thanks very much,
>> Sharon
>
> You do know that the first 'C' in CIC stands for "cascaded", yes?

I think that he is referring to is using multiple CIC stages instead of
one. Sure, for each stage, you cascade a couple of Combs and Integrators.

I think this is fine. I can imagine that for a rather huge decimation
like 4000X this will work better than doing a single-stage "CIC
decimation" because increasing the order of a single-stage further
beyond a certain point has only little effect w.r.t. the lowpass
filter's characteristics.

```
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# Re: Combining multiple CIC decimation filters in series - SRB - 2012-10-31 13:47:00

```Hi

>You do know that the first 'C' in CIC stands for "cascaded", yes?

Yes, but what I'm considering is not just cascading the integrators and
combs but also decimating more than once (so it would effectively be a

>If the math works out, and the resulting spectrum is what you want,
>what's not to like?

There are a couple of things I don't really like:
1) I haven't found much reference to doing this in the literature which
makes me think that it is not done very much and that there is probably a
good reason for that...
2) If I'm going to cascade CICs that opens up a whole series of other
questions about how many to use and what decimation factors they should
have, so actually I'm hoping to discover that it is not a good idea so I
don't have to address those questions!

Thanks again,
Sharon

```
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# Re: Combining multiple CIC decimation filters in series - SRB - 2012-10-31 13:56:00

```Hi SG

>I think that he is referring to is using multiple CIC stages instead of
>one. Sure, for each stage, you cascade a couple of Combs and Integrators.

Yes, you're right - that's what I'm referring to.

>I think this is fine. I can imagine that for a rather huge decimation
>like 4000X this will work better than doing a single-stage "CIC
>decimation" because increasing the order of a single-stage further
>beyond a certain point has only little effect w.r.t. the lowpass
>filter's characteristics.

What I seem to be finding so far is that I can't improve total aliased
power by cascading more than one CIC because aliasing occurs each time you
decimate (so even though stopband attenuation for each CIC is better, total
aliased power for all CICs combined is not). However, it does seem that I
can reduce the number of operations per input sample by having multiple
CICs if I'm prepared to accept a slight increase in aliased power, because
the first CIC can be of lower order while still having good stopband
attenuation.

It does surprise me that I'm not finding papers on this though...

Thanks again,
Sharon
```
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# Re: Combining multiple CIC decimation filters in series - dbd - 2012-10-31 21:31:00

```On Wednesday, October 31, 2012 10:56:26 AM UTC-7, SRB wrote:
> Hi SG
> ...
>
> It does surprise me that I'm not finding papers on this though...
>
>
>
> Thanks again,
>
> Sharon

Have you tried Google? The words:

multiple stage cic filter

get such things as:

http://www.indjst.org/archive/vol.4.issue.8/18-aug11anilsingh.pdf
Multistage implementation of multirate CIC filters
Anil Singh, Poonam Singhal and Rajeev Ratan

.pdf

and many more...

Have you tried the multiple stage method that these sources illustrate?

Dale B. Dalrymple
```
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# Re: Combining multiple CIC decimation filters in series - robert bristow-johnson - 2012-11-01 01:27:00

```On 10/31/12 9:21 AM, Tim Wescott wrote:
>   I'm just a control systems guy,

who writes books with DSP in them.

> where CIC filters do not prevail.

moving averages are never useful for smoothing something (say the set
point if it moves around) in control systems?

> If the math works out, and the resulting spectrum is what you want,
> what's not to like?
>

--

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

```
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# Re: Combining multiple CIC decimation filters in series - SRB - 2012-11-01 09:04:00

```>Have you tried Google? The words:
>
>multiple stage cic filter

Hi Dale

Thank you very much for your suggestion. In many of the links found by this
search the term 'multiple stage' or 'multi-stage' refers either to using
CICs with more than one integrator/comb pair or to combining a CIC with
FIRs, rather than to combining several decimating CICs in series, which is
what I was looking for. However, I did find a couple of relevant references
using this search, so thanks very much! :-)

Sharon
```
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# Re: Combining multiple CIC decimation filters in series - dbd - 2012-11-01 12:54:00

```On Wednesday, October 31, 2012 6:45:09 AM UTC-7, SRB wrote:
> Hi All
> ...
> So my questions are:
>
>
>
> 1) Do people typically combine multiple CIC filters in series in this way?
>
> and if not, why not?
>
> 2) Are there any guidelines or rules of thumb as to how to select the
>
> number of filters to use and what decimation factor to use in each? (e.g.
>
> any publications similar to that of Crochiere and Rabiner 1975 for FIRs)
>
>
>
>
> Thanks very much,
>
> Sharon

Except perhaps in comp.dsp, it is common for engineers to compare alternate signal processing
approaches by the resources required to achieve a filtering requirement (passband accuracy,
transition band width, stopband attenuation) as well as the resampling ratio. Since CICs are
often noted for poor passband accuracy, they are combined with other filters to realize some
complete filter specification.

A classic example of a design process aimed at achieving  a filter specification with resampling
is the Goodman-Carey paper:

IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL. ASSP-2S, NO.2, APRIL 1977
Nine Digital Filters for Decimation and Interpolation
DAVID J. GOODMAN, MEMBER, IEEE, AND MICHAEL J. CAREY

Whether the Goodman-Carey or any similar approach would be effective for your application
measures of resource cost: multiplies, adds, registers, logic blocks, etc.). Goodman-Carey
combines CICs with additional halfband filters. YMMV.

How did you pick multiple stages of CIC/resampler blocks?

Dale B. Dalrymple
```
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# Re: Combining multiple CIC decimation filters in series - Dave - 2012-11-01 13:15:00

```On Nov 1, 12:54 pm, dbd <d...@ieee.org> wrote:
> On Wednesday, October 31, 2012 6:45:09 AM UTC-7, SRB wrote:
> > Hi All
> > ...
> > So my questions are:
>
> > 1) Do people typically combine multiple CIC filters in series in this way?
>
> > and if not, why not?
>
> > 2) Are there any guidelines or rules of thumb as to how to select the
>
> > number of filters to use and what decimation factor to use in each? (e.g.
>
> > any publications similar to that of Crochiere and Rabiner 1975 for FIRs)
>
> > Any thoughts/opinions/suggestions gratefully received.
>
> > Thanks very much,
>
> > Sharon
>
> Except perhaps in comp.dsp, it is common for engineers to compare alternate signal
processing approaches by the resources required to achieve a filtering requirement (passband
accuracy, transition band width, stopband attenuation) as well as the resampling ratio. Since
CICs are often noted for poor passband accuracy, they are combined with other filters to realize
some complete filter specification.
>
> A classic example of a design process aimed at achieving  a filter specification with
resampling is the Goodman-Carey paper:
>
> IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL. ASSP-2S, NO.2, APRIL
1977
> Nine Digital Filters for Decimation and Interpolation
> DAVID J. GOODMAN, MEMBER, IEEE, AND MICHAEL J. CAREY
>
> Whether the Goodman-Carey or any similar approach would be effective for your application
measures of resource cost: multiplies, adds, registers, logic blocks, etc.). Goodman-Carey
combines CICs with additional halfband filters. YMMV.
>
> How did you pick multiple stages of CIC/resampler blocks?
>
> Dale B. Dalrymple

Another alternative is to look at the Graychip documentation. The
Graychip is a configurable chip which consists of  basebanding
capability  followed by CIC and then followed by 2 FIR downsampling
filters (if memory serves correctly). In the documentation they give
several configurations which meet specific communication standards.

In their documentation they typically use the first FIR to compensate
for the CIC passband, and the 2nd FIR to provide further downsampling
and  attenuation.

Cheers,
Dave
```
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