Forums

Multirate filter

Started by alexgaas November 25, 2009
Hi everybody!
I'm working on a UWB radar and i have an analog front end that samples the
input signal in a nonuniform way.
For the reconstruction filter i would use a nonuniform reconstruction
algorithm from IEEE transaction on signal processing.These are links : 

http://www.rle.mit.edu/dspg/documents/00Eldar.pdf

webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf

The second link is the case for periodic signal, the only difference is in
the low-pass filter that is sinx/x in the first case while sin(Mx)/sin(x)
in the second one.
At page 11-12 and 13 there is the scheme of the multirate filter that is
necessary.
The impulse response of this filter is a summation of N scaled and shifted
version of low pass one (you can see an example in figure 6).
What are an efficient implementation of this kind of filter??
In my application N could be very large from 10 to 100.
So i need 100 FIR filter??Is there other implementation more efficient
(not necessary in time domain)?? 

Thanks a lot!
On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote:
> Hi everybody! > I'm working on a UWB radar and i have an analog front end that samples the > input signal in a nonuniform way. > For the reconstruction filter i would use a nonuniform reconstruction > algorithm from IEEE transaction on signal processing.These are links : > > http://www.rle.mit.edu/dspg/documents/00Eldar.pdf > > webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf > > The second link is the case for periodic signal, the only difference is in > the low-pass filter that is sinx/x in the first case while sin(Mx)/sin(x) > in the second one. > At page 11-12 and 13 there is the scheme of the multirate filter that is > necessary. > The impulse response of this filter is a summation of N scaled and shifted > version of low pass one (you can see an example in figure 6). > What are an efficient implementation of this kind of filter?? > In my application N could be very large from 10 to 100. > So i need 100 FIR filter??Is there other implementation more efficient > (not necessary in time domain)??
I've worked out all the details to this and written a short summary. It's available here: http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing_samples.pdf Some more info, including Matlab code to design an run the reconstruction filters is availabler here: http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip The reconstruction filters can be FIR filters (they all are, up to some modulation, fractional delay filters) which can efficiently be computed in frequency domain. If I remember correctly, Mark Borgerding also wrote a DSP Tips & Tricks article on efficient implementation of FIR filterbanks in frequency domain. Regards, Andor
>On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote: >> Hi everybody! >> I'm working on a UWB radar and i have an analog front end that samples
the
>> input signal in a nonuniform way. >> For the reconstruction filter i would use a nonuniform reconstruction >> algorithm from IEEE transaction on signal processing.These are links : >> >> http://www.rle.mit.edu/dspg/documents/00Eldar.pdf >> >> webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf >> >> The second link is the case for periodic signal, the only difference is
in
>> the low-pass filter that is sinx/x in the first case while
sin(Mx)/sin(x)
>> in the second one. >> At page 11-12 and 13 there is the scheme of the multirate filter that
is
>> necessary. >> The impulse response of this filter is a summation of N scaled and
shifted
>> version of low pass one (you can see an example in figure 6). >> What are an efficient implementation of this kind of filter?? >> In my application N could be very large from 10 to 100. >> So i need 100 FIR filter??Is there other implementation more efficient >> (not necessary in time domain)?? > >I've worked out all the details to this and written a short summary. >It's available here: > >http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing_samples.pdf > >Some more info, including Matlab code to design an run the >reconstruction filters is availabler here: > >http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip > >The reconstruction filters can be FIR filters (they all are, up to >some modulation, fractional delay filters) which can efficiently be >computed in frequency domain. If I remember correctly, Mark Borgerding >also wrote a DSP Tips & Tricks article on efficient implementation of >FIR filterbanks in frequency domain. > >Regards, >Andor >
Thanks a lot!!
>On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote: >> Hi everybody! >> I'm working on a UWB radar and i have an analog front end that samples
the
>> input signal in a nonuniform way. >> For the reconstruction filter i would use a nonuniform reconstruction >> algorithm from IEEE transaction on signal processing.These are links : >> >> http://www.rle.mit.edu/dspg/documents/00Eldar.pdf >> >> webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf >> >> The second link is the case for periodic signal, the only difference is
in
>> the low-pass filter that is sinx/x in the first case while
sin(Mx)/sin(x)
>> in the second one. >> At page 11-12 and 13 there is the scheme of the multirate filter that
is
>> necessary. >> The impulse response of this filter is a summation of N scaled and
shifted
>> version of low pass one (you can see an example in figure 6). >> What are an efficient implementation of this kind of filter?? >> In my application N could be very large from 10 to 100. >> So i need 100 FIR filter??Is there other implementation more efficient >> (not necessary in time domain)?? > >I've worked out all the details to this and written a short summary. >It's available here: > >http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing_samples.pdf > >Some more info, including Matlab code to design an run the >reconstruction filters is availabler here: > >http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip > >The reconstruction filters can be FIR filters (they all are, up to >some modulation, fractional delay filters) which can efficiently be >computed in frequency domain. If I remember correctly, Mark Borgerding >also wrote a DSP Tips & Tricks article on efficient implementation of >FIR filterbanks in frequency domain. > >Regards, >Andor >
Another question... What are performance of these algorithms in noisy environment especially for very high bandwidth (several GHz) where the jitter noise is dominant?? For my radar jitter is a problem because with recurrent nonuniform sampling we can't resample in the same time istants. So is not possible acquire for an istant 100 points to remove noise with averaging. If someone have ideas to overcome this problem (averaging after nonuniform reconstruction) could be great! Regards, Alex
On 28 Nov., 18:07, "alexgaas" <alex_g...@hotmail.com> wrote:
> >On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote: > >> Hi everybody! > >> I'm working on a UWB radar and i have an analog front end that samples > the > >> input signal in a nonuniform way. > >> For the reconstruction filter i would use a nonuniform reconstruction > >> algorithm from IEEE transaction on signal processing.These are links : > > >>http://www.rle.mit.edu/dspg/documents/00Eldar.pdf > > >> webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf > > >> The second link is the case for periodic signal, the only difference is > in > >> the low-pass filter that is sinx/x in the first case while > sin(Mx)/sin(x) > >> in the second one. > >> At page 11-12 and 13 there is the scheme of the multirate filter that > is > >> necessary. > >> The impulse response of this filter is a summation of N scaled and > shifted > >> version of low pass one (you can see an example in figure 6). > >> What are an efficient implementation of this kind of filter?? > >> In my application N could be very large from 10 to 100. > >> So i need 100 FIR filter??Is there other implementation more efficient > >> (not necessary in time domain)?? > > >I've worked out all the details to this and written a short summary. > >It's available here: > > >http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing... > > >Some more info, including Matlab code to design an run the > >reconstruction filters is availabler here: > > >http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip > > >The reconstruction filters can be FIR filters (they all are, up to > >some modulation, fractional delay filters) which can efficiently be > >computed in frequency domain. If I remember correctly, Mark Borgerding > >also wrote a DSP Tips & Tricks article on efficient implementation of > >FIR filterbanks in frequency domain. > > >Regards, > >Andor > > Another question... > What are performance of these algorithms in noisy environment especially > for very high bandwidth (several GHz) where the jitter noise is dominant??
You can read about this here: http://www.eng.tau.ac.il/~meir/publication/seidner02noiseamp.pdf Regards, Andor
Andor wrote:
> On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote: >> Hi everybody! >> I'm working on a UWB radar and i have an analog front end that samples the >> input signal in a nonuniform way. >> For the reconstruction filter i would use a nonuniform reconstruction >> algorithm from IEEE transaction on signal processing.These are links : >> >> http://www.rle.mit.edu/dspg/documents/00Eldar.pdf >> >> webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf >> >> The second link is the case for periodic signal, the only difference is in >> the low-pass filter that is sinx/x in the first case while sin(Mx)/sin(x) >> in the second one. >> At page 11-12 and 13 there is the scheme of the multirate filter that is >> necessary. >> The impulse response of this filter is a summation of N scaled and shifted >> version of low pass one (you can see an example in figure 6). >> What are an efficient implementation of this kind of filter?? >> In my application N could be very large from 10 to 100. >> So i need 100 FIR filter??Is there other implementation more efficient >> (not necessary in time domain)?? > > I've worked out all the details to this and written a short summary. > It's available here: > > http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing_samples.pdf > > Some more info, including Matlab code to design an run the > reconstruction filters is availabler here: > > http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip > > The reconstruction filters can be FIR filters (they all are, up to > some modulation, fractional delay filters) which can efficiently be > computed in frequency domain. If I remember correctly, Mark Borgerding > also wrote a DSP Tips & Tricks article on efficient implementation of > FIR filterbanks in frequency domain.
What is being reconstructed? The reconstruction filters I know of remove the stair-step shape from the output of DACs and possibly correct for the sin(x)/x rolloff at high frequencies. Those are necessarily analog. Is there an analog FIR filter? Switched-capacitor, maybe? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On 30 Nov., 02:01, Jerry Avins <j...@ieee.org> wrote:
> Andor wrote: > > On 25 Nov., 21:57, "alexgaas" <alex_g...@hotmail.com> wrote: > >> Hi everybody! > >> I'm working on a UWB radar and i have an analog front end that samples the > >> input signal in a nonuniform way. > >> For the reconstruction filter i would use a nonuniform reconstruction > >> algorithm from IEEE transaction on signal processing.These are links : > > >>http://www.rle.mit.edu/dspg/documents/00Eldar.pdf > > >> webee.technion.ac.il/Sites/People/YoninaEldar/Info/70.pdf > > >> The second link is the case for periodic signal, the only difference is in > >> the low-pass filter that is sinx/x in the first case while sin(Mx)/sin(x) > >> in the second one. > >> At page 11-12 and 13 there is the scheme of the multirate filter that is > >> necessary. > >> The impulse response of this filter is a summation of N scaled and shifted > >> version of low pass one (you can see an example in figure 6). > >> What are an efficient implementation of this kind of filter?? > >> In my application N could be very large from 10 to 100. > >> So i need 100 FIR filter??Is there other implementation more efficient > >> (not necessary in time domain)?? > > > I've worked out all the details to this and written a short summary. > > It's available here: > > >http://www.zhaw.ch/~bara/files/recovering_periodically_spaced_missing... > > > Some more info, including Matlab code to design an run the > > reconstruction filters is availabler here: > > >http://www.zhaw.ch/~bara/files/Recover_Missing_Samples.zip > > > The reconstruction filters can be FIR filters (they all are, up to > > some modulation, fractional delay filters) which can efficiently be > > computed in frequency domain. If I remember correctly, Mark Borgerding > > also wrote a DSP Tips & Tricks article on efficient implementation of > > FIR filterbanks in frequency domain. > > What is being reconstructed? The reconstruction filters I know of remove > the stair-step shape from the output of DACs and possibly correct for > the sin(x)/x rolloff at high frequencies. Those are necessarily analog. > Is there an analog FIR filter? Switched-capacitor, maybe?
If I understood Alex correctly, he wants to resample a non-uniformly sampled sequence into a uniformly sampled sequence ("reconstruct" the uniform from the non-uniform case), under certain bandwidth constraints for the continuous-time signal that was (non-uniformly) sampled. The condition is that the non-uniform sampling pattern is periodic. You can read the DSP Tips & Tricks article that I linked, where this process is explained in detail. Regards, Andor
On Sun, 29 Nov 2009 20:01:23 -0500, Jerry Avins <jya@ieee.org> wrote:

>What is being reconstructed? The reconstruction filters I know of remove >the stair-step shape from the output of DACs and possibly correct for >the sin(x)/x rolloff at high frequencies. Those are necessarily analog. >Is there an analog FIR filter? Switched-capacitor, maybe?
I once have seen a semi-analog FIR-Filter. A serial bit stream had its spectrum formed before modulating it on a carrier by clocking it through a shift register and summing the taps with a fast inverting op amp. The resistors coming from the SR taps to the summing node represented the filter coefficients. Look, Ma, no coils, no precision caps! With a LC delay line or a tapped cable this could be extended to true analog inputs, other than 0 and 3.3 Volts. regards, Gerhard