FIR interpolator

"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message 
news:_PzBj.15715$Ej5.2369@newssvr29.news.prodigy.net...
>
> Recently I run into the problem with a basic task: design of a polyphase 
> set of filters for the interpolation of a signal. The input is the sampled 
> signal; the output should be the interpolated values spaced at 1/10 of the 
> sample.
>
> So, I designed the LPF at 10 x sample rate by the Parks-McClellan 
> algorithm, and then decimated it into 10 subsets of the coefficients.
>
> But, although the original filter is well within the specs, the decimated 
> subsets (calculated to the original sample rate) are not! There is a 
> significant difference is in the passband flatness as well as in the 
> stopband.
>
> Where is the mistake?
>
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultant
> http://www.abvolt.com
>

Vladimir,

I'm not sure I understand what you're doing yet.  You can't just take any 
filter and make it polyphase.  The essential ingredient is that only certain 
coefficients contribute to the output at each output sample instant.  Once 
that's ascertained then the filter can be split into "phases" leading to a 
polyphase / parallel sort of implementation.  Otherwise it can't.

A classical halfband filter meets this criterion because (nearly) half of 
the coefficients are zero and equispaced.  Thus one shift of the half the 
input samples contribute to the output and one delay later the opposite 
input samples contribute to the output.  So, one can construct two filter 
paths that add at the output.

It's not proper to simply skip multiplies that are in the original filter 
design.

But, perhaps I missed the point?

Fred

Fred 

On Mar 11, 12:16 pm, dbell <bellda2...@cox.net> wrote:
> On Mar 11, 3:58 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
> wrote:
> > Vladimir Vassilevsky wrote:
>
> > > Recently I run into the problem with a basic task: design of a polyphase
> > > set of filters for the interpolation of a signal. The input is the
> > > sampled signal; the output should be the interpolated values spaced at
> > > 1/10 of the sample.
>
> > > So, I designed the LPF at 10 x sample rate by the Parks-McClellan
> > > algorithm, and then decimated it into 10 subsets of the coefficients.
>
> > > But, although the original filter is well within the specs, the
> > > decimated subsets (calculated to the original sample rate) are not!
> > > There is a significant difference is in the passband flatness as well as
> > > in the stopband.
>
> > > Where is the mistake?
>
> > What happens: when the original interpolator LPF response is decimated
> > by the factor of N, its stopband gets aliased by the factor of N also.
> > This alters the frequency response of the subset filters. So, if it is
> > desired to keep the passband flatness, then the stopband attenuation of
> > the original filter has to be increased. In the worst case, the increase
> > should be by the factor of N, however you can probably get by the
> > smaller factors.
>
> > Thanks to everybody! The question is clear now.
>
> > Vladimir Vassilevsky
> > DSP and Mixed Signal Design Consultanthttp://www.abvolt.com-Hide quoted text -
>
> > - Show quoted text -
>
> If the net effect is a flat passband on the whole filter, what is the
> concern about the individual partial filters?

1)
They give you a properly filtered or interpolated partial
sample tapped delay line, or 1/10th sample delay element.

2)
If the result from the full filter is properly bandlimited
to below 1/20th the new sample rate, then subsampling that
new bandlimited signal at or above 1/10th the new sample
rate should produce results that allow reconstruction of
the original signal.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

On Mar 11, 4:36&#4294967295;pm, "Ron N." <rhnlo...@yahoo.com> wrote:
> On Mar 11, 12:16 pm, dbell <bellda2...@cox.net> wrote:
>
>
>
>
>
> > On Mar 11, 3:58 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
> > wrote:
> > > Vladimir Vassilevsky wrote:
>
> > > > Recently I run into the problem with a basic task: design of a polyphase
> > > > set of filters for the interpolation of a signal. The input is the
> > > > sampled signal; the output should be the interpolated values spaced at
> > > > 1/10 of the sample.
>
> > > > So, I designed the LPF at 10 x sample rate by the Parks-McClellan
> > > > algorithm, and then decimated it into 10 subsets of the coefficients.
>
> > > > But, although the original filter is well within the specs, the
> > > > decimated subsets (calculated to the original sample rate) are not!
> > > > There is a significant difference is in the passband flatness as well as
> > > > in the stopband.
>
> > > > Where is the mistake?
>
> > > What happens: when the original interpolator LPF response is decimated
> > > by the factor of N, its stopband gets aliased by the factor of N also.
> > > This alters the frequency response of the subset filters. So, if it is
> > > desired to keep the passband flatness, then the stopband attenuation of
> > > the original filter has to be increased. In the worst case, the increase
> > > should be by the factor of N, however you can probably get by the
> > > smaller factors.
>
> > > Thanks to everybody! The question is clear now.
>
> > > Vladimir Vassilevsky
> > > DSP and Mixed Signal Design Consultanthttp://www.abvolt.com-Hidequoted text -
>
> > > - Show quoted text -
>
> > If the net effect is a flat passband on the whole filter, what is the
> > concern about the individual partial filters?
>
> 1)
> They give you a properly filtered or interpolated partial
> sample tapped delay line, or 1/10th sample delay element.
>
> 2)
> If the result from the full filter is properly bandlimited
> to below 1/20th the new sample rate, then subsampling that
> new bandlimited signal at or above 1/10th the new sample
> rate should produce results that allow reconstruction of
> the original signal.
>
> IMHO. YMMV.
> --
> rhn A.T nicholson d.0.t C-o-M- Hide quoted text -
>
> - Show quoted text -

And would that not be true anyway if the original filter was
appropriately designed, without caring exactly how the partial filters
looked?

Dirk

On Mar 11, 1:10 pm, dbell <bellda2...@cox.net> wrote:
> On Mar 11, 4:36 pm, "Ron N." <rhnlo...@yahoo.com> wrote:
>
>
>
> > On Mar 11, 12:16 pm, dbell <bellda2...@cox.net> wrote:
>
> > > On Mar 11, 3:58 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
> > > wrote:
> > > > Vladimir Vassilevsky wrote:
>
> > > > > Recently I run into the problem with a basic task: design of a polyphase
> > > > > set of filters for the interpolation of a signal. The input is the
> > > > > sampled signal; the output should be the interpolated values spaced at
> > > > > 1/10 of the sample.
>
> > > > > So, I designed the LPF at 10 x sample rate by the Parks-McClellan
> > > > > algorithm, and then decimated it into 10 subsets of the coefficients.
>
> > > > > But, although the original filter is well within the specs, the
> > > > > decimated subsets (calculated to the original sample rate) are not!
> > > > > There is a significant difference is in the passband flatness as well as
> > > > > in the stopband.
>
> > > > > Where is the mistake?
>
> > > > What happens: when the original interpolator LPF response is decimated
> > > > by the factor of N, its stopband gets aliased by the factor of N also.
> > > > This alters the frequency response of the subset filters. So, if it is
> > > > desired to keep the passband flatness, then the stopband attenuation of
> > > > the original filter has to be increased. In the worst case, the increase
> > > > should be by the factor of N, however you can probably get by the
> > > > smaller factors.
>
> > > > Thanks to everybody! The question is clear now.
>
> > > > Vladimir Vassilevsky
> > > > DSP and Mixed Signal Design Consultanthttp://www.abvolt.com-Hidequotedtext -
>
> > > > - Show quoted text -
>
> > > If the net effect is a flat passband on the whole filter, what is the
> > > concern about the individual partial filters?
>
> > 1)
> > They give you a properly filtered or interpolated partial
> > sample tapped delay line, or 1/10th sample delay element.
>
> > 2)
> > If the result from the full filter is properly bandlimited
> > to below 1/20th the new sample rate, then subsampling that
> > new bandlimited signal at or above 1/10th the new sample
> > rate should produce results that allow reconstruction of
> > the original signal.
>
> > IMHO. YMMV.
> > --
> > rhn A.T nicholson d.0.t C-o-M- Hide quoted text -
>
> > - Show quoted text -
>
> And would that not be true anyway if the original filter was
> appropriately designed, without caring exactly how the partial filters
> looked?

The question appears to be how to appropriately design
the original filter if you actually do care about the output
of the partial filters (as would be the case if you were
using them as a selectable delay elements, or some-such.)

e.g. If have a given Passband specification for the
partial filters, is it affected by the Stopband spec in
the undecimated full filter?  Looks like it might be.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

On Tue, 11 Mar 2008 13:22:03 -0700, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> wrote:

>I'm not sure I understand what you're doing yet.  You can't just take any 
>filter and make it polyphase.  The essential ingredient is that only certain 
>coefficients contribute to the output at each output sample instant.  Once 
>that's ascertained then the filter can be split into "phases" leading to a 
>polyphase / parallel sort of implementation.  Otherwise it can't.

I'm not convinced that's strictly true.  Generally you're using a
polyphase filter to resample by M/N, with certain restrictions on the
common factors of M and N.  Under these circumstances you're
'conceptually' upsampling to LCM(M,N) (LCM = least common multiple),
anti-alias filtering as appropriate, and decimating.  With a polyphase
filter, in this situation, I believe that you'll need the output from
every phase at one point in time or another, just not *all* of them
*all* of the time.  And I think that any old filter will suffice for
the polyphase implementation, provided that it meets the anti-aliasing
criteria when implemented at the LCM sampling rate.

Vladimir appears to be doing something different.  It looks like he's
keeping his original sampling rate, but shifting his sampling times
1/10 sample period by interpolating.  In this case he's really only
using one phase of his polyphase filter, and throwing the other nine
away.  So for this I think he just needs a filter that works better
after its coefficients have been decimated.

>A classical halfband filter meets this criterion because (nearly) half of 
>the coefficients are zero and equispaced.  Thus one shift of the half the 
>input samples contribute to the output and one delay later the opposite 
>input samples contribute to the output.  So, one can construct two filter 
>paths that add at the output.
>
>It's not proper to simply skip multiplies that are in the original filter 
>design.

If you were to construct the two decimated filters extracted from the
two "halves" of the halfband filter, their frequency responses would
be dissimilar due to aliasing.  Their sum would be okay, but each one
individually would not look exactly like the desired overall response.
This is similar to what Vladimir is apparently observing.

Greg

On Tue, 11 Mar 2008 13:22:03 -0700, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> wrote:

>
>"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message 
>news:_PzBj.15715$Ej5.2369@newssvr29.news.prodigy.net...
>>
>> Recently I run into the problem with a basic task: design of a polyphase 
>> set of filters for the interpolation of a signal. The input is the sampled 
>> signal; the output should be the interpolated values spaced at 1/10 of the 
>> sample.
>>
>> So, I designed the LPF at 10 x sample rate by the Parks-McClellan 
>> algorithm, and then decimated it into 10 subsets of the coefficients.
>>
>> But, although the original filter is well within the specs, the decimated 
>> subsets (calculated to the original sample rate) are not! There is a 
>> significant difference is in the passband flatness as well as in the 
>> stopband.
>>
>> Where is the mistake?
>>
>>
>> Vladimir Vassilevsky
>> DSP and Mixed Signal Design Consultant
>> http://www.abvolt.com
>>
>
>Vladimir,
>
>I'm not sure I understand what you're doing yet.  You can't just take any 
>filter and make it polyphase.  The essential ingredient is that only certain 
>coefficients contribute to the output at each output sample instant.  Once 
>that's ascertained then the filter can be split into "phases" leading to a 
>polyphase / parallel sort of implementation.  Otherwise it can't.
>
>A classical halfband filter meets this criterion because (nearly) half of 
>the coefficients are zero and equispaced.  Thus one shift of the half the 
>input samples contribute to the output and one delay later the opposite 
>input samples contribute to the output.  So, one can construct two filter 
>paths that add at the output.
>
>It's not proper to simply skip multiplies that are in the original filter 
>design.
>
>But, perhaps I missed the point?
>
>Fred

Having built resampling polyphase filters with arbitrary coefficients
(i.e., read from RAM), that had all sorts of coefficient sets in
practical use, both symmetric and minimum-phase, I don't think your
assertion is accurate.  As long as the filter is reasonably designed
to avoid aliasing under the configured resampling conditions and the
coefficients were adequately oversampled, it's a fairly generalized
problem.

At least in our case everything always worked as expected, and we did
some weird stuff with it.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

On Mar 12, 9:56 am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
> On Tue, 11 Mar 2008 13:22:03 -0700, "Fred Marshall"
>
>
>
> <fmarshallx@remove_the_x.acm.org> wrote:
>
> >"Vladimir Vassilevsky" <antispam_bo...@hotmail.com> wrote in message
> >news:_PzBj.15715$Ej5.2369@newssvr29.news.prodigy.net...
>
> >> Recently I run into the problem with a basic task: design of a polyphase
> >> set of filters for the interpolation of a signal. The input is the sampled
> >> signal; the output should be the interpolated values spaced at 1/10 of the
> >> sample.
>
> >> So, I designed the LPF at 10 x sample rate by the Parks-McClellan
> >> algorithm, and then decimated it into 10 subsets of the coefficients.
>
> >> But, although the original filter is well within the specs, the decimated
> >> subsets (calculated to the original sample rate) are not! There is a
> >> significant difference is in the passband flatness as well as in the
> >> stopband.
>
> >> Where is the mistake?
>
> >> Vladimir Vassilevsky
> >> DSP and Mixed Signal Design Consultant
> >>http://www.abvolt.com
>
> >Vladimir,
>
> >I'm not sure I understand what you're doing yet.  You can't just take any
> >filter and make it polyphase.  The essential ingredient is that only certain
> >coefficients contribute to the output at each output sample instant.  Once
> >that's ascertained then the filter can be split into "phases" leading to a
> >polyphase / parallel sort of implementation.  Otherwise it can't.
>
> >A classical halfband filter meets this criterion because (nearly) half of
> >the coefficients are zero and equispaced.  Thus one shift of the half the
> >input samples contribute to the output and one delay later the opposite
> >input samples contribute to the output.  So, one can construct two filter
> >paths that add at the output.
>
> >It's not proper to simply skip multiplies that are in the original filter
> >design.
>
> >But, perhaps I missed the point?
>
> >Fred
>
> Having built resampling polyphase filters with arbitrary coefficients
> (i.e., read from RAM), that had all sorts of coefficient sets in
> practical use, both symmetric and minimum-phase, I don't think your
> assertion is accurate.  As long as the filter is reasonably designed
> to avoid aliasing under the configured resampling conditions and the
> coefficients were adequately oversampled, it's a fairly generalized
> problem.
>
> At least in our case everything always worked as expected, and we did
> some weird stuff with it.

Were you concerned about extreme flatness in the passband?

I think the key difference might be that Vladimir was
concerned about passband ripple after proper decimation or
subsampling.  Subsampling a properly but imperfectly
bandlimited signal (e.g. new Fs > Bw*2, but the bandlimit
filter length was finite) causes the a portion of the
filter stopband ripple to affect the resulting passband
ripple.  One needs to find the overlapping portions of
the repeated filter spectra, and perhaps use tighter
constraints on those segments of the bandlimit filter.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
 http://www.nicholson.com/rhn/dsp.html

Ron N. wrote:

>>>"Vladimir Vassilevsky" <antispam_bo...@hotmail.com> wrote in message
>>>news:_PzBj.15715$Ej5.2369@newssvr29.news.prodigy.net...
>>
>>>>Recently I run into the problem with a basic task: design of a polyphase
>>>>set of filters for the interpolation of a signal. The input is the sampled
>>>>signal; the output should be the interpolated values spaced at 1/10 of the
>>>>sample.
>>
>>>>So, I designed the LPF at 10 x sample rate by the Parks-McClellan
>>>>algorithm, and then decimated it into 10 subsets of the coefficients.
>>
>>>>But, although the original filter is well within the specs, the decimated
>>>>subsets (calculated to the original sample rate) are not! There is a
>>>>significant difference is in the passband flatness as well as in the
>>>>stopband.
>>
> I think the key difference might be that Vladimir was
> concerned about passband ripple after proper decimation or
> subsampling.


My goal was a variable delay line with a resolution of 1/10 of a sample. 
So I am using just one of the subsets of the coefficients of the x10 
interpolation filter at a time. It was quite unexpected to find out that 
the frequency response of a subset filter in the passband could be very 
different from that of the complete interpolation filter.

I don't know what should be the exact design procedure, however it looks 
like for the worst case the interpolator filter by N should have lower 
stopband by the factor of N also. I guess you have to do several 
iterations adjusting the stopband.



Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Mar 12, 11:03 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> Ron N. wrote:
> >>>"Vladimir Vassilevsky" <antispam_bo...@hotmail.com> wrote in message
> >>>news:_PzBj.15715$Ej5.2369@newssvr29.news.prodigy.net...
>
> >>>>Recently I run into the problem with a basic task: design of a polyphase
> >>>>set of filters for the interpolation of a signal. The input is the sampled
> >>>>signal; the output should be the interpolated values spaced at 1/10 of the
> >>>>sample.
>
> >>>>So, I designed the LPF at 10 x sample rate by the Parks-McClellan
> >>>>algorithm, and then decimated it into 10 subsets of the coefficients.
>
> >>>>But, although the original filter is well within the specs, the decimated
> >>>>subsets (calculated to the original sample rate) are not! There is a
> >>>>significant difference is in the passband flatness as well as in the
> >>>>stopband.
>
> > I think the key difference might be that Vladimir was
> > concerned about passband ripple after proper decimation or
> > subsampling.
>
> My goal was a variable delay line with a resolution of 1/10 of a sample.

That was my guess.

> So I am using just one of the subsets of the coefficients of the x10
> interpolation filter at a time. It was quite unexpected to find out that
> the frequency response of a subset filter in the passband could be very
> different from that of the complete interpolation filter.

Subsampling (by 1/10th) in the time domain repeats the
filter's frequency response in the frequency domain.
The resultant subset filter is the sum of those overlapped
spectra.  Only if there is no overlap (Nyquist) and the
stopband level is zero will the new frequency response
be identical.

> I don't know what should be the exact design procedure, however it looks
> like for the worst case the interpolator filter by N should have lower
> stopband by the factor of N also. I guess you have to do several
> iterations adjusting the stopband.

Try finding those segments of the stopband that overlaps
the passband in the repeated spectra, and only constrain
those smaller portions lower.  e.g. equiripple with notches.
Might result in a shorter filter.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
 http://www.nicholson.com/rhn/dsp.html

On Mar 12, 5:23 pm, "Ron N." <rhnlo...@yahoo.com> wrote:
...
> Try finding those segments of the stopband that overlaps
> the passband in the repeated spectra, and only constrain
> those smaller portions lower.  e.g. equiripple with notches.

i thought i said as much.  if you have notches to -inf dB at integer
multiples of Fs, then, at least at DC, there won't be any difference
between the different phases.

> Might result in a shorter filter.

if you compare apples to apples with the same length filter, there is
a slight trade off with the first and biggest stopband lobe.

> IMHO.

my O, too.

r b-j