# Impulse response of multirate system?

Started by September 24, 2008
```Hi,

I was wondering if impulse response of multirate system is defined and
can be evaluated? I built a CIC decimator in Matlab, the differential delay
is 1, downsample factor is 8. # of stage is 2, transfer function is
[(1-Z^-8)/(1-Z^-1)]^2. I realize it is a LTV system. Anyone has idea on how
to simulate impulse response of it, not deriving it on paper?

cfy30

```
```On Sep 24, 9:08&#4294967295;am, "cfy30" <cf...@yahoo.com> wrote:
> Hi,
>
> &#4294967295; I was wondering if impulse response of multirate system is defined and
> can be evaluated? I built a CIC decimator in Matlab, the differential delay
> is 1, downsample factor is 8. # of stage is 2, transfer function is
> [(1-Z^-8)/(1-Z^-1)]^2. I realize it is a LTV system. Anyone has idea on how
> to simulate impulse response of it, not deriving it on paper?
>
> cfy30

What have you done so far?

Did you try putting an impulse in at a number of different shifts?
Did the results make any sense?

Are you expecting the impulse response to characterize the whole thing
so you can convolve the impulse response with the input to get the
output? Where does the downsampling fit in then? Is what you are doing
going to generate the aliasing that you will get?  Is the aliasing far
enough down that you don't care about it?

Does the normal addition of filter after the CIC make any difference
to what you are trying to accomplish?

Is the impulse response of the whole CIC filter really what you want?

Dirk
```
```The CIC is built in simulink. integrator and differentiator outputs are
monitored, everything works as expected.

Impulse with different delay was sent to the filter, outputs do not
resemble the sinc shape.

Downsampling is, of course, happens between the integrator and
differentiator blocks. What's your idea on placing the downsampler?

Aliasing? What do you mean? Aren't all LTI system can be characterized by
the output response with impulse input. Why aliasing is a concern here?

What I want to see is the sinc shape as derived, but through simulation.

cfy30

>On Sep 24, 9:08=A0am, "cfy30" <cf...@yahoo.com> wrote:
>> Hi,
>>
>> =A0 I was wondering if impulse response of multirate system is defined
an=
>d
>> can be evaluated? I built a CIC decimator in Matlab, the differential
del=
>ay
>> is 1, downsample factor is 8. # of stage is 2, transfer function is
>> [(1-Z^-8)/(1-Z^-1)]^2. I realize it is a LTV system. Anyone has idea on
h=
>ow
>> to simulate impulse response of it, not deriving it on paper?
>>
>> cfy30
>
>What have you done so far?
>
>Did you try putting an impulse in at a number of different shifts?
>Did the results make any sense?
>
>Are you expecting the impulse response to characterize the whole thing
>so you can convolve the impulse response with the input to get the
>output? Where does the downsampling fit in then? Is what you are doing
>going to generate the aliasing that you will get?  Is the aliasing far
>enough down that you don't care about it?
>
>Does the normal addition of filter after the CIC make any difference
>to what you are trying to accomplish?
>
>Is the impulse response of the whole CIC filter really what you want?
>
>Dirk
>
```
```You have some reading to do. Hogenauer's paper, or Frerking's book.
Do a search here for other references or a more detailed description.
Or try the math.

Why are you expecting a sinc shape? That is for a perfect LP. A CIC LP
is a poor filter that performs "well" only if you are highly
oversampled. . When you decimate you get aliasing.  You don't have an
LTI system. Is the impulse response characterizing your system? It
appears not. Is it time-invariant?  You need to look at the steps in
the process and analyze the steps, and figure out why aliasing is a
concern.

Dirk

cfy30 wrote:
> The CIC is built in simulink. integrator and differentiator outputs are
> monitored, everything works as expected.
>
> Impulse with different delay was sent to the filter, outputs do not
> resemble the sinc shape.
>
> Downsampling is, of course, happens between the integrator and
> differentiator blocks. What's your idea on placing the downsampler?
>
> Aliasing? What do you mean? Aren't all LTI system can be characterized by
> the output response with impulse input. Why aliasing is a concern here?
>
> What I want to see is the sinc shape as derived, but through simulation.
>
>
> cfy30
>
>
> >On Sep 24, 9:08=A0am, "cfy30" <cf...@yahoo.com> wrote:
> >> Hi,
> >>
> >> =A0 I was wondering if impulse response of multirate system is defined
> an=
> >d
> >> can be evaluated? I built a CIC decimator in Matlab, the differential
> del=
> >ay
> >> is 1, downsample factor is 8. # of stage is 2, transfer function is
> >> [(1-Z^-8)/(1-Z^-1)]^2. I realize it is a LTV system. Anyone has idea on
> h=
> >ow
> >> to simulate impulse response of it, not deriving it on paper?
> >>
> >> cfy30
> >
> >What have you done so far?
> >
> >Did you try putting an impulse in at a number of different shifts?
> >Did the results make any sense?
> >
> >Are you expecting the impulse response to characterize the whole thing
> >so you can convolve the impulse response with the input to get the
> >output? Where does the downsampling fit in then? Is what you are doing
> >going to generate the aliasing that you will get?  Is the aliasing far
> >enough down that you don't care about it?
> >
> >Does the normal addition of filter after the CIC make any difference
> >to what you are trying to accomplish?
> >
> >Is the impulse response of the whole CIC filter really what you want?
> >
> >Dirk
> >
```
```Shouldn't "sin(Mx/2)/sin(x/2)" resemable sinc shape?

"Is the impulse response characterizing your system?"?! This is my
question, and I am looking for the answer.

Nevertheless, thank you very much for the replies.

cfy30

>You have some reading to do. Hogenauer's paper, or Frerking's book.
>Do a search here for other references or a more detailed description.
>Or try the math.
>
>Why are you expecting a sinc shape? That is for a perfect LP. A CIC LP
>is a poor filter that performs "well" only if you are highly
>oversampled. . When you decimate you get aliasing.  You don't have an
>LTI system. Is the impulse response characterizing your system? It
>appears not. Is it time-invariant?  You need to look at the steps in
>the process and analyze the steps, and figure out why aliasing is a
>concern.
>
>Dirk
>
>cfy30 wrote:
>> The CIC is built in simulink. integrator and differentiator outputs
are
>> monitored, everything works as expected.
>>
>> Impulse with different delay was sent to the filter, outputs do not
>> resemble the sinc shape.
>>
>> Downsampling is, of course, happens between the integrator and
>> differentiator blocks. What's your idea on placing the downsampler?
>>
>> Aliasing? What do you mean? Aren't all LTI system can be characterized
by
>> the output response with impulse input. Why aliasing is a concern
here?
>>
>> What I want to see is the sinc shape as derived, but through
simulation.
>>
>>
>> cfy30
>>
>>
>> >On Sep 24, 9:08=A0am, "cfy30" <cf...@yahoo.com> wrote:
>> >> Hi,
>> >>
>> >> =A0 I was wondering if impulse response of multirate system is
defined
>> an=
>> >d
>> >> can be evaluated? I built a CIC decimator in Matlab, the
differential
>> del=
>> >ay
>> >> is 1, downsample factor is 8. # of stage is 2, transfer function is
>> >> [(1-Z^-8)/(1-Z^-1)]^2. I realize it is a LTV system. Anyone has idea
on
>> h=
>> >ow
>> >> to simulate impulse response of it, not deriving it on paper?
>> >>
>> >> cfy30
>> >
>> >What have you done so far?
>> >
>> >Did you try putting an impulse in at a number of different shifts?
>> >Did the results make any sense?
>> >
>> >Are you expecting the impulse response to characterize the whole
thing
>> >so you can convolve the impulse response with the input to get the
>> >output? Where does the downsampling fit in then? Is what you are
doing
>> >going to generate the aliasing that you will get?  Is the aliasing
far
>> >enough down that you don't care about it?
>> >
>> >Does the normal addition of filter after the CIC make any difference
>> >to what you are trying to accomplish?
>> >
>> >Is the impulse response of the whole CIC filter really what you want?
>> >
>> >Dirk
>> >
>
```
```On Sep 25, 12:00&#4294967295;am, "cfy30" <cf...@yahoo.com> wrote:
> Shouldn't "sin(Mx/2)/sin(x/2)" resemable sinc shape? &#4294967295;
>
> "Is the impulse response characterizing your system?"?! This is my
> question, and I am looking for the answer. &#4294967295;
>
> Nevertheless, thank you very much for the replies.
>
> cfy30
>
<CLIPPED>

It is sort of sinc shaped. However is that in the time domain or
frequency domain? It does not include the decimation (producing
aliasing) included in the end-to-end CIC filter.

Take a look at

http://www.embedded.com/columns/showArticle.jhtml?articleID=160400592

by comp.dsp's very own Rick Lyons.

It might give you a better idea what to expect.

Dirk
```
```On Thu, 25 Sep 2008 00:37:49 -0700 (PDT), dbell <bellda2005@cox.net>
wrote:

>On Sep 25, 12:00=A0am, "cfy30" <cf...@yahoo.com> wrote:
>> Shouldn't "sin(Mx/2)/sin(x/2)" resemable sinc shape? =A0
>>
>> "Is the impulse response characterizing your system?"?! This is my
>> question, and I am looking for the answer. =A0
>>
>> Nevertheless, thank you very much for the replies.
>>
>> cfy30
>>
><CLIPPED>
>
>It is sort of sinc shaped. However is that in the time domain or
>frequency domain? It does not include the decimation (producing
>aliasing) included in the end-to-end CIC filter.
>
>Take a look at
>
>http://www.embedded.com/columns/showArticle.jhtml?articleID=3D160400592
>
>by comp.dsp's very own Rick Lyons.
>
>It might give you a better idea what to expect.
>
>Dirk

Hi Dirk,
if the above link doesn't work, cfy30 might try:

http://www.embedded.com/columns/technicalinsights/160400592?_requestid=59523

Regards,
[-Rick-]

```
```On Sep 25, 6:54&#4294967295;am, R.Lyons@_Bogus_ieee.org (Rick Lyons) wrote:
> On Thu, 25 Sep 2008 00:37:49 -0700 (PDT), dbell <bellda2...@cox.net>
> wrote:
>
>
>
>
>
> >On Sep 25, 12:00=A0am, "cfy30" <cf...@yahoo.com> wrote:
> >> Shouldn't "sin(Mx/2)/sin(x/2)" resemable sinc shape? =A0
>
> >> "Is the impulse response characterizing your system?"?! This is my
> >> question, and I am looking for the answer. =A0
>
> >> Nevertheless, thank you very much for the replies.
>
> >> cfy30
>
> ><CLIPPED>
>
> >It is sort of sinc shaped. However is that in the time domain or
> >frequency domain? It does not include the decimation (producing
> >aliasing) included in the end-to-end CIC filter.
>
> >Take a look at
>
> >http://www.embedded.com/columns/showArticle.jhtml?articleID=3D160400592
>
> >by comp.dsp's very own Rick Lyons.
>
> >It might give you a better idea what to expect.
>
> >Dirk
>
> Hi Dirk,
> &#4294967295; if the above link doesn't work, cfy30 might try:
>
> http://www.embedded.com/columns/technicalinsights/160400592?_requesti...
>
> Regards,
> [-Rick-]- Hide quoted text -
>
> - Show quoted text -

Hi Rick,

The link worked last night.

Dirk
```