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

# Impulse response of multirate system?

Started by ●September 24, 2008

Reply by ●September 24, 20082008-09-24

On Sep 24, 9:08�am, "cfy30" <cf...@yahoo.com> wrote:> 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? > > cfy30What 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

Reply by ●September 24, 20082008-09-24

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 definedan=>d >> can be evaluated? I built a CIC decimator in Matlab, the differentialdel=>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 onh=>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 >

Reply by ●September 24, 20082008-09-24

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 > >

Reply by ●September 25, 20082008-09-25

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 outputsare>> 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 characterizedby>> the output response with impulse input. Why aliasing is a concernhere?>> >> What I want to see is the sinc shape as derived, but throughsimulation.>> >> >> cfy30 >> >> >> >On Sep 24, 9:08=A0am, "cfy30" <cf...@yahoo.com> wrote: >> >> Hi, >> >> >> >> =A0 I was wondering if impulse response of multirate system isdefined>> an= >> >d >> >> can be evaluated? I built a CIC decimator in Matlab, thedifferential>> 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 ideaon>> 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 wholething>> >so you can convolve the impulse response with the input to get the >> >output? Where does the downsampling fit in then? Is what you aredoing>> >going to generate the aliasing that you will get? Is the aliasingfar>> >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 >> > >

Reply by ●September 25, 20082008-09-25

On Sep 25, 12:00�am, "cfy30" <cf...@yahoo.com> wrote:> 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 ><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

Reply by ●September 25, 20082008-09-25

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. > >DirkHi Dirk, if the above link doesn't work, cfy30 might try: http://www.embedded.com/columns/technicalinsights/160400592?_requestid=59523 Regards, [-Rick-]

Reply by ●September 25, 20082008-09-25

On Sep 25, 6:54�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, > � 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