Polyphase in Practice

Started by Fred Marshall March 24, 2005
As some may have noticed, I have a particular interest in frequency 
multiplication filtering methods - among other things.  So, you can imagine 
my slight bias when looking at polyphase filters.

I think Rick Lyon's book puts polyphase filters into a very nice 
perspective!  I highly recommend it to all.

In doing filtering in "batch" mode I can imagine a (temporal) "polyphase" 
filter as nothing but a FIR filter with certain characteristics that lead to 
a smart implementation in software - an algorithm if you will.  And, I can 
assume that the implementer is clever enough to figure this out.  That 
given, the polyphase filter is just another FIR filter.  [This is just a 
perspective - not anything profound].

So, if polyphase implementation isn't such a big deal in software and isn't 
operative at all in frequency multiplying implementation then when is it?  I 
can imagine an FPGA temporal implementation might benefit.  So, is that it? 
Is there more to be said about it?

For that matter, has anyone read the latest IEEE Signal Processing Trans. by 
Lim et al regarding efficient implementation of interpolation filters?  Any 
comments?  Some of the response plots remind me of things that are 
"supergained" so I wonder how robust these designs are......

Thanks,

Fred






On Thu, 24 Mar 2005 11:04:43 -0800, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> wrote:

>As some may have noticed, I have a particular interest in frequency >multiplication filtering methods - among other things. So, you can imagine >my slight bias when looking at polyphase filters. > >I think Rick Lyon's book puts polyphase filters into a very nice >perspective! I highly recommend it to all. > >In doing filtering in "batch" mode I can imagine a (temporal) "polyphase" >filter as nothing but a FIR filter with certain characteristics that lead to >a smart implementation in software - an algorithm if you will. And, I can >assume that the implementer is clever enough to figure this out. That >given, the polyphase filter is just another FIR filter. [This is just a >perspective - not anything profound]. > >So, if polyphase implementation isn't such a big deal in software and isn't >operative at all in frequency multiplying implementation then when is it? I >can imagine an FPGA temporal implementation might benefit. So, is that it? >Is there more to be said about it? > >For that matter, has anyone read the latest IEEE Signal Processing Trans. by >Lim et al regarding efficient implementation of interpolation filters? Any >comments? Some of the response plots remind me of things that are >"supergained" so I wonder how robust these designs are...... > >Thanks, > >Fred
I'm not sure that I'm following you exactly, but polyphase filters are very useful for any application where output samples must be generated asynchronous to the input sample stream. In other words, if you need to interpolate at arbitrary or highly granular intervals between the input samples, a polyphase is a great beast with which to solve the problem. That applies to interpolation or decimation...if you need a slightly different output rate than input rate, or, more generally, non-integer multiples of the input rate, then "just another FIR filter" becomes a slightly more complicated FIR filter. It's still just a FIR filter, but selection of the coefficients and their quantity departs from the trivial case. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
On Thu, 24 Mar 2005 11:04:43 -0800, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> wrote:

>As some may have noticed, I have a particular interest in frequency >multiplication filtering methods - among other things. So, you can imagine >my slight bias when looking at polyphase filters.
Hi Fred, humm, I wonder what you mean by "frequency multiplication filtering methods". Maybe you're referring to multiplication in the frequency domain to implement convolution in the time doamin.
>I think Rick Lyon's book puts polyphase filters into a very nice >perspective! I highly recommend it to all.
Ah, thanks for the kind words. Coming from a guy like you, they mean a lot to me.
>In doing filtering in "batch" mode I can imagine a (temporal) "polyphase" >filter as nothing but a FIR filter with certain characteristics that lead to >a smart implementation in software - an algorithm if you will. And, I can >assume that the implementer is clever enough to figure this out. That >given, the polyphase filter is just another FIR filter. [This is just a >perspective - not anything profound]. > >So, if polyphase implementation isn't such a big deal in software and isn't >operative at all in frequency multiplying implementation then when is it? I >can imagine an FPGA temporal implementation might benefit. So, is that it? >Is there more to be said about it?
(snipped) I've always thought of polyphase filters (the FIR-type) as being very clever implementations that avoid: 1) computing filter output samples that we intend to discard in a decimation application, and 2) all the multiplications by zero-valued samples in an interpolation application. In different words, I've always viewed polyphase FIR filters as a super computationally-efficient way to perform linear-phase lowpass filtering in multirate applications. Stated in strictly technical terms, "polyphase filters are lean, mean, fat-free, filtering machines." See Ya', [-Rick-] And yes, I own a George Forman lean mean fat-free grilling machine. (I'm a bachelor.)
Fred Marshall wrote:
> > For that matter, has anyone read the latest IEEE Signal Processing Trans. by > Lim et al regarding efficient implementation of interpolation filters? Any > comments?
Fred, Would you be able to post the complete title and author information. I don't have regular access to IEEE Trans on SP, but occassionally pay for and article via IEEE-explore. This paper looks like one that I may be interested in. TIA, Erik PS : Sorry I don't have anything intelligent to say about the polyphase issue :-). -- +-----------------------------------------------------------+ Erik de Castro Lopo nospam@mega-nerd.com (Yes it's valid) +-----------------------------------------------------------+ "These are the finest moments in (post)modern life, when satire is completly indistinguishable from reality... I usually have to rely on the presidential elections for such dada." -- frenomulax on Jesux a christian Linux distro.
in article 42435100.6121B41B@mega-nerd.com, Erik de Castro Lopo at
nospam@mega-nerd.com wrote on 03/24/2005 18:45:

> Would you be able to post the complete title and author information. > I don't have regular access to IEEE Trans on SP, but occassionally pay for > and article via IEEE-explore. This paper looks like one that I may be > interested in.
i wouldn't mind a pdf copy if someone has it. (my interest isn't so great that i want to pay IEEE $$ for it.)
> PS : Sorry I don't have anything intelligent to say about the polyphase issue > :-).
really! no secret rabbits to pull out of your hat? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
in article 424340aa.202358187@news.sf.sbcglobal.net, Rick Lyons at
r.lyons@_BOGUS_ieee.org wrote on 03/24/2005 17:54:

> In different words, I've always viewed > polyphase FIR filters as a super computationally-efficient > way to perform linear-phase lowpass filtering in > multirate applications. > > Stated in strictly technical terms, "polyphase filters are > lean, mean, fat-free, filtering machines."
i just look at it as a *collection* of FIR filters, each with incremental fractional (plus some fixed integer to make them causal) delay and as flat magnitude response as we can get. whether we use it for sample rate conversion, fractional delay filtering, or some other interpolation, that's all i use "polyphase filters" for. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
"Erik de Castro Lopo" <nospam@mega-nerd.com> wrote in message 
news:42435100.6121B41B@mega-nerd.com...
> Fred Marshall wrote: >> >> For that matter, has anyone read the latest IEEE Signal Processing Trans. >> by >> Lim et al regarding efficient implementation of interpolation filters? >> Any >> comments? > > Fred, > > Would you be able to post the complete title and author information. > I don't have regular access to IEEE Trans on SP, but occassionally pay for > and article via IEEE-explore. This paper looks like one that I may be > interested in. > > TIA, > Erik
IEEE Trans SP April 2005, Vol 53, No. 4 ITPRED (ISSN-1053-587X) pp. 1387-1397. "On the Synthesis of Very Sharp Decimators and Interpolators Using the Frequency-Response Masking Technique" Y.C. Lim and R. Yang
"Rick Lyons" <r.lyons@_BOGUS_ieee.org> wrote in message 
news:424340aa.202358187@news.sf.sbcglobal.net...
> On Thu, 24 Mar 2005 11:04:43 -0800, "Fred Marshall" > <fmarshallx@remove_the_x.acm.org> wrote: > >>As some may have noticed, I have a particular interest in frequency >>multiplication filtering methods - among other things. So, you can >>imagine >>my slight bias when looking at polyphase filters. > > Hi Fred, > > humm, I wonder what you mean by "frequency multiplication > filtering methods". Maybe you're referring to > multiplication in the frequency domain to implement > convolution in the time doamin.
Yep, I was.
"robert bristow-johnson" <rbj@audioimagination.com> wrote in message 
news:BE68CFCA.5934%rbj@audioimagination.com...
> in article 424340aa.202358187@news.sf.sbcglobal.net, Rick Lyons at > r.lyons@_BOGUS_ieee.org wrote on 03/24/2005 17:54: > >> In different words, I've always viewed >> polyphase FIR filters as a super computationally-efficient >> way to perform linear-phase lowpass filtering in >> multirate applications. >> >> Stated in strictly technical terms, "polyphase filters are >> lean, mean, fat-free, filtering machines." > > i just look at it as a *collection* of FIR filters, each with incremental > fractional (plus some fixed integer to make them causal) delay and as flat > magnitude response as we can get. >
rb-j, I don't get the part about flat magnitude response. That must be some property I've not focused on. Fred
in article c8CdnY7OTKPd7t7fRVn-qA@centurytel.net, Fred Marshall at
fmarshallx@remove_the_x.acm.org wrote on 03/24/2005 21:11:

> "robert bristow-johnson" <rbj@audioimagination.com> wrote in message > news:BE68CFCA.5934%rbj@audioimagination.com...
...
>> i just look at it as a *collection* of FIR filters, each with incremental >> fractional (plus some fixed integer to make them causal) delay and as flat >> magnitude response as we can get. >> > > rb-j, > > I don't get the part about flat magnitude response. > That must be some property I've not focused on.
i guess it doesn't *have* to be flat, but to be honest, i really don't have a concept of the application of the polyphase filter concept except for doing intersample interpolation, which is usually for use in sample rate conversion or a (sub-sample) precision delay. in these applications, there isn't any reason that i can think of that you would want to change anything else (such as magnitude) other than the delay. when i use MATLAB's remez() or firls() to design a set of polyphase filters, one design goal is flat frequency response for each polyphase coefficient set. i dunno. when is not-flat frequency response desirable? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."