Data-path accuracy in IIR filters?
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From: gretzteam on 30 Jul 2010 00:03 >>>I did a quick search on "digital lattice filter" and didn't come up with >>>any really coherent discussion. There was lots of stuff about how to >>>use this or that lattice filter in this or that specialized application, >>>but not "this is DF1, this is DF2, this is a digital lattice filter...". > >>>Got any references? > >>Hi Tim, >>I`ve sucessfully used this Matlab toolbox to design various lattice/wave >>filters. > >What's a wave filter? >S. Here you go: http://www.dsprelated.com/showmessage/31630/1.php The paper from L. Gazsi is very interesting and easy to follow. Dave
From: Rune Allnor on 30 Jul 2010 03:12 On 30 Jul, 01:42, Tim Wescott <t...(a)seemywebsite.com> wrote: > On 07/29/2010 12:47 PM, Steve Pope wrote: > > > > > > > Pete Fraser<pfra...(a)covad.net> wrote: > > >> I am working on a project where I need to > >> implement 6-th order Butterworth low-pass > >> filters in an FPGA. In some the bandwidth is > >> low relative to the input data rate, whereas > >> others have higher bandwidth. I can use ScopeIIR > >> or Matlab to give me a good idea of coefficient > >> accuracy for any given ratio of bandwidth to > >> input sample rate. > > >> However, I'm not sure what data-path accuracy > >> I need (for 20-bit input / output accuracy). > >> Is there a rule-of-thumb I can use, or do I just > >> have to simulate the filter with real data and > >> see what gives me low enough noise? > > > You should simulate the fixed-point filter. When simulating, > > you do not necessarily have to stimulate it with realistic data. I > > often will stimulate the design being tested with bandlimited noise, and > > measure the RMS error of output (relative to the same design, but in full > > floating-point). Plotting the RMS error (in dBc) vs. RMS input level > > gives you a very good idea of the dynamic range of the fixed point > > design. > > >> I was planning on using biquads, but I'm not sure > >> whether I'm better off with DF1 or DF2 sections. > > > You can do this, or you can use a lattice topology > > (called "ARMA" in matlab/fdatool), which is the most > > well-behaved topology. > > > Steve > > I did a quick search on "digital lattice filter" and didn't come up with > any really coherent discussion. There was lots of stuff about how to > use this or that lattice filter in this or that specialized application, > but not "this is DF1, this is DF2, this is a digital lattice filter...". > > Got any references? These filters are treated in medium / advanced level DSP books, like Proakis & Manolakis. Don't think the term 'lattice filter' is too common, though; rather 'lattice structure' or 'lattice ladder structure'. I am not sure they are worth a general discussion: The problem is that the lattice structure fuses both the FIR and its IIR inverse, so if the FIR has zeros on or outside the unit circle, the computations blow up. It makes a lot of sense keeping those disussion on a need to know basis. Rune
From: Steve Pope on 30 Jul 2010 12:31 Rune Allnor <allnor(a)tele.ntnu.no> wrote: >On 30 Jul, 01:42, Tim Wescott <t...(a)seemywebsite.com> wrote: >> On 07/29/2010 12:47 PM, Steve Pope wrote: >> > You can do this, or you can use a lattice topology >> I did a quick search on "digital lattice filter" and didn't come up with >> any really coherent discussion. �There was lots of stuff about how to >> use this or that lattice filter in this or that specialized application, >> but not "this is DF1, this is DF2, this is a digital lattice filter...". >> Got any references? >These filters are treated in medium / advanced level >DSP books, like Proakis & Manolakis. Don't think the >term 'lattice filter' is too common, though; rather >'lattice structure' or 'lattice ladder structure'. >I am not sure they are worth a general discussion: >The problem is that the lattice structure fuses both >the FIR and its IIR inverse, so if the FIR has zeros on >or outside the unit circle, the computations blow up. I do not think this is a problem in practice. The FIR form of any topology is stable; the IIR form of the lattice topology is unconditionally stable if the coefficients are in the range (-1,1) and you are using saturating arithmetic. This latter fact makes them very useful in implementation, because (almost) any IIR filter you would want to implement satisfies this constraint. >It makes a lot of sense keeping those disussion on a >need to know basis. Just FYI, the lattice topology is my first-line choice for implementing a typical IIR such as the OP's Butterworth. I only go to something else if the lattice topology it too costly (it does take 3*N+1 multiplies to implement a N-pole, N-zero filter. But often the multipliers are somewhat lower precision than in other topologies; the coefficients tend to be pretty insensitive.) I have used these filters many, many times because the design time is really short because you don't have to angst over whether you've chosen a well-behaved structure. Steve
From: gretzteam on 30 Jul 2010 12:48 >Just FYI, the lattice topology is my first-line choice >for implementing a typical IIR such as the OP's Butterworth. >I only go to something else if the lattice topology it >too costly (it does take 3*N+1 multiplies to implement >a N-pole, N-zero filter. But often the multipliers are >somewhat lower precision than in other topologies; >the coefficients tend to be pretty insensitive.) >I have used these filters many, many times because the >design time is really short because you don't have >to angst over whether you've chosen a well-behaved structure. > >Steve > Same here. You can usually blindly quantize the coefficients to something like 12 bits and still keep the frequency response almost unchanged. However I usually struggle trying to pick the best allpass structure. There are like 23 different versions, first and second order, with each their own pros/cons. Dave
From: Steve Pope on 30 Jul 2010 14:46
Rune Allnor <allnor(a)tele.ntnu.no> wrote: >These filters are treated in medium / advanced level >DSP books, like Proakis & Manolakis. Don't think the >term 'lattice filter' is too common, though; rather >'lattice structure' or 'lattice ladder structure'. Also, I'm pretty sure the "wave filters" or "wave lattice filters" are not closely related to (what I am calling) a lattice filter or lattice structure. "lattice-ladder" specifically refers to the topology of this family that gives you both poles and zeros. Steve |