Pete Fraser wrote:
> "Steve Pope" <spope33@speedymail.org> wrote in message 
> news:i3p8af$btu$1@blue.rahul.net...
>> Pete Fraser <pfraser@covad.net> wrote:
> 
>>> Perhaps we're talking at cross purposes here, or there's something
>>> I don't understand. The Magnitude response estimate is -80 dB
>>> at DC. It should be 0 dB in the passband.
>> Okay that's not good.
>>
>> But it looked okay in full floating point?
> 
> Yes.
> 
>> Do you have the option of quantizing just the coefficients, and
>> not the data path?  That is the first step.
> 
> Unfortunately not.
> 
>>> It does. I need 6th order, and 96 dB dynamic range, but I've
>>> been setting FDATool to much greater coefficient accuracies and
>>> data-path resolutions than you're suggesting. There must be some
>>> aspect of the tool I'm not understanding (or, as Rick Lyons suggested,
>>> there are problems with it).
>> Yes, it's not sure it is worth the time to sort this out, when
>> you have just one filter to design.
> 
> I've got many filters to design (on this project).
> Also, I think Matlab will be a good tool for future projects.
> In the past almost all my projects were video.
> Recently I've been doing audio and data acquisition, hence the
> interest in IIR.
> 
>> The (full-precision) coefficients
>> themselves are probably good; and you can just go with them in a design.
>> However it seems the tool is not helping you make other design
>> decisions, such as DF vs. ARMA, or helping you study precisions.
> 
> The Matlab sales guy said that I could do a phone conference with
> a Matlab support guy if I needed talked through something.
> Maybe I'll take him up on that.
> 
> Pete 
> 
> 

Hi Pete,

The FDATool and filterbuilder GUIs do static range analysis. This works 
well to convert FIR filters to fixed-point but because of their 
recursive nature, IIR filters are difficult to fine tune without running 
data through them.

If you are comfortable with MATLAB, you can either export your design 
from FDATool/filterbuilder (or start your design with fdesign.lowpass) 
and use the autoscale() and qreport() functions to perform dynamic range 
analysis. Here is a demo to get started with the conversion of an IIR 
filter from floating-point to fixed-point:

http://www.mathworks.com/products/filterdesign/demos.html?file=/products/demos/shipping/filterdesign/iirfloat2fixeddemo.html

The demo uses a Chebyshev Type I design but you can simply replace 
'cheby1' with 'butter' to experiment with Butterworth designs.

A second demo might be of interest if you want to compare different 
structures (e.g. DF1SOS vs. DF2SOS):

http://www.mathworks.com/products/filterdesign/demos.html?file=/products/demos/shipping/filterdesign/iirautoscaledemo.html

Hope this helps,

Vincent

On Aug 7, 9:26&#4294967295;pm, "Pete Fraser" <pfra...@covad.net> wrote:
> I'm new to Matlab, and to IIR design, so
> sorry in advance if these questions are dumb.
>

there are no dumb questions, just dumb cliches.

> I've been playing with filterbuilder and FDATool
> just to get familiar with the options / design flow.
> There seems to be a lot of overlap.
>
> Why would somebody want to use filterbuilder rather
> the FDATool?

dunno.  i haven't used either.

> Say I design a 6th order, DFII Butterworth LPF,
> with Fs = 48000 and Fc = 10800.
>
> I do a fixed point quantization with the default settings.
> Input word length is 16, and input fraction length 15.

okay, right here is a little problem.  if you have double-wide (32
bit) words for the product of 16x16 multiplication, and if you can add
those numbers full precision until you're done and then quantize to 16
bit, then you should not use DF2.  you should use DF1 instead.  your
6th-order filter will have 8 states instead of 6 (big deeeel) but
you'll do much better in terms of signal quantization error and
saturation error, particularly if the filter is resonant (which each
section of the Butterworth is).

> I assume that means that the input is considered to run
> from -1.0 to +(2^15 -1)/2^15. Is that correct?

sure, why not?  as far as the signal is concerned, it's just a scaling
factor.  and the same for the feedforward coefficients {b0, b1, b2}.
but, for the feedback coefs {a1, a2}, their scale matters.  although |
a2| is less than 1 (for a stable filter), |a1| can be nearly as big as
2.

> When the "avoid overflow" box on the output is checked,
> it seems to operate as a 16 bit output with a fraction length
> of ten bits. Why is that? I would have assumed that, if the
> input is considered to have one bit before the point, then
> the output would need two bits to accommodate
> overshoots in the step response. Why are six bits needed?

it might not be a step response that causes the worst overflow.  a
resonant filter can have much greater gain (as the resonant frequency)
than even 5 extra guard bits will accommodate.  but it's not likely.

> I'm not sure what the Magnitude Response Estimate does.
> I'm guessing it shows the difference between a white
> pseudo-noise input and the associated output spectrum.
> The response in the stop-band is a combination of the actual
> frequency response, and the stop-band noise caused by
> pass-band components being quantized. Is that right?

dunno, i'd just be guessing.

r b-j

Pete Fraser <pfraser@covad.net> wrote:

>"Steve Pope" <spope33@speedymail.org> wrote in message 

>> Pete Fraser <pfraser@covad.net> wrote:

>>>Perhaps we're talking at cross purposes here, or there's something
>>>I don't understand. The Magnitude response estimate is -80 dB
>>>at DC. It should be 0 dB in the passband.

>> Okay that's not good.

>> But it looked okay in full floating point?

>Yes.

>> Do you have the option of quantizing just the coefficients, and
>> not the data path?  That is the first step.

>Unfortunately not.

For the tool to be useful, it must let you conduct experiments
in the right order.  It sounds like it does not allow this,
or at least you haven't figured out how to coerce it into doing so.

It does not take too long to write, in MATLAB or C or C++, functions
to quantize double precision floating point values into
IEEE 1666 fixed-point values in one or two of the most useful
modes ("saturating, rounding" mode being the single most useful
for your purposes; it is often reasaonable to do an entire design
in just this mode).  Or you can dig around online for such code.

There is only an issue if your fixed-point words exceed 52 bits
wide in which case they cannot be directly stored in a double.

>The Matlab sales guy said that I could do a phone conference with
>a Matlab support guy if I needed talked through something.
>Maybe I'll take him up on that.

That's a good plan.  If you go through that excercise, and it
still is not doing what you want, that's a bad sign for the tool.

Steve

"Steve Pope" <spope33@speedymail.org> wrote in message 
news:i3p8af$btu$1@blue.rahul.net...
> Pete Fraser <pfraser@covad.net> wrote:

>>Perhaps we're talking at cross purposes here, or there's something
>>I don't understand. The Magnitude response estimate is -80 dB
>>at DC. It should be 0 dB in the passband.
>
> Okay that's not good.
>
> But it looked okay in full floating point?

Yes.

> Do you have the option of quantizing just the coefficients, and
> not the data path?  That is the first step.

Unfortunately not.

>>It does. I need 6th order, and 96 dB dynamic range, but I've
>>been setting FDATool to much greater coefficient accuracies and
>>data-path resolutions than you're suggesting. There must be some
>>aspect of the tool I'm not understanding (or, as Rick Lyons suggested,
>>there are problems with it).
>
> Yes, it's not sure it is worth the time to sort this out, when
> you have just one filter to design.

I've got many filters to design (on this project).
Also, I think Matlab will be a good tool for future projects.
In the past almost all my projects were video.
Recently I've been doing audio and data acquisition, hence the
interest in IIR.

> The (full-precision) coefficients
> themselves are probably good; and you can just go with them in a design.
> However it seems the tool is not helping you make other design
> decisions, such as DF vs. ARMA, or helping you study precisions.

The Matlab sales guy said that I could do a phone conference with
a Matlab support guy if I needed talked through something.
Maybe I'll take him up on that.

Pete 

Pete Fraser <pfraser@covad.net> wrote:

>"Steve Pope" <spope33@speedymail.org> wrote in message 

>> Pete Fraser <pfraser@covad.net> wrote:

>>>but converting to fixed point with the
>>>tool's defaults gives me a Magnitude Response Estimate of about -80 dB
>>>from DC to Nyquist. Doubling the number of bits everywhere gives me
>>>an MRE of -140 dB from DC to Nyquist (note, this is Magnitude
>>>Response Estimate -- not Noise Power Spectrum).

>> I don't necessarily see the above as bad results, other than the
>> non-controllability of the tool,

>Perhaps we're talking at cross purposes here, or there's something
>I don't understand. The Magnitude response estimate is -80 dB
>at DC. It should be 0 dB in the passband.

Okay that's not good.

But it looked okay in full floating point?

Do you have the option of quantizing just the coefficients, and
not the data path?  That is the first step.  

What precision coefficients results in a 80 dB response error at DC?

>It does. I need 6th order, and 96 dB dynamic range, but I've
>been setting FDATool to much greater coefficient accuracies and
>data-path resolutions than you're suggesting. There must be some
>aspect of the tool I'm not understanding (or, as Rick Lyons suggested,
>there are problems with it).

Yes, it's not sure it is worth the time to sort this out, when
you have just one filter to design.  The (full-precision) coefficients
themselves are probably good; and you can just go with them in a design.
However it seems the tool is not helping you make other design 
decisions, such as DF vs. ARMA, or helping you study precisions.

Steve

"Steve Pope" <spope33@speedymail.org> wrote in message 
news:i3nu2p$u18$1@blue.rahul.net...
> Pete Fraser <pfraser@covad.net> wrote:

>>but converting to fixed point with the
>>tool's defaults gives me a Magnitude Response Estimate of about -80 dB
>>from DC to Nyquist. Doubling the number of bits everywhere gives me
>>an MRE of -140 dB from DC to Nyquist (note, this is Magnitude
>>Response Estimate -- not Noise Power Spectrum).
>
> I don't necessarily see the above as bad results, other than the
> non-controllability of the tool,

Perhaps we're talking at cross purposes here, or there's something
I don't understand. The Magnitude response estimate is -80 dB
at DC. It should be 0 dB in the passband.

> but I do not know your dynamic
> range requirements.  Maybe you have extreme requirements and will
> need to use floating point arithmetic in your implementation;
> that sometimes happens.

I don't think so. 96 dB should be fine.
I've got ample FPGA, and the data rate is slow, so I can go to very
high fixed-point accuracy if I need to.

> The last time I had to design a comparable Butterworth filter, it required
> a dynamic range of about 80 dB, and I ended up with the following
> precisions in a lattice (ARMA) structure: 22 bit internal data, and 12
> bit coefficients.  This was a 4th order filter with a passband
> of 0.01 * Fs.  The internal data values required four additional
> bits to the left of the binary point than did the input value.
> This seems (roughly) comparable to what you're trying to do.

It does. I need 6th order, and 96 dB dynamic range, but I've
been setting FDATool to much greater coefficient accuracies and
data-path resolutions than you're suggesting. There must be some
aspect of the tool I'm not understanding (or, as Rick Lyons suggested,
there are problems with it).

> As I mentioned, I like to plot RMS error (in dBc) vs. input signal level
> (in dB relative to some nominal level) to visualize quantization
> effects.  Such a plot should typically have a flat floor in the middle of
> the usable range (representing the limits of your coefficient
> quantization; this includes your stop-band artifacts); it should have a
> 6 dB/octave slope in the lower-signal range (resulting from the data-path
> quantization); and a steep saturating effect at high signal levels.  If
> you do not obtain this sort of U-shaped or V-shaped curve, something is
> seriously wrong.

I'll give that a try.
Do you use Matlab for this?
If so, what toolboxes do you need?

The Mathworks is going to want money from me soon, and
I'll need to decide what tool boxes to buy.
>
> (I do not think this is one of the plots fdatool likes to spit out on
> its own.)

It's not.

Thanks

Pete 

Steve Pope <spope33@speedymail.org> wrote:

>it should have a 
>6 dB/octave slope in the lower-signal range (resulting from the data-path 
>quantization); 

Oops.. meant to say a slope of one (6dB per 6dB).


S.

Pete Fraser <pfraser@covad.net> wrote:

>Things get worse when I go to higher accuracy and narrower filters.
>If I start looking at a filter with f3db = 0.05, things get messy. The 
>response
>is ugly, the stop-band artifacts are extremely high, and the tool does
>things I don't expect. It doesn't seem to default to higher accuracy in the
>data path for narrower filters, but when I change to higher accuracy the
>performance gets much worse. I'm not sure if the tool is broken, I'm
>ignorant, or a combination of the two (wierd rendering bugs in the GUI don't
>fill me with confidence though.).

>I seem to get bad results with any architecture. DF2SOS is weird, but
>I tried Steve's earlier suggestion of ARMA, and converted a 6th
>order Butterworth LPF with f3db = 0.05 to ARMA. The floating
>point response looks fine, but converting to fixed point with the
>tool's defaults gives me a Magnitude Response Estimate of about -80 dB
>from DC to Nyquist. Doubling the number of bits everywhere gives me
>an MRE of -140 dB from DC to Nyquist (note, this is Magnitude
>Response Estimate -- not Noise Power Spectrum).

I don't necessarily see the above as bad results, other than the
non-controllability of the tool, but I do not know your dynamic
range requirements.  Maybe you have extreme requirements and will
need to use floating point arithmetic in your implementation;
that sometimes happens.

The last time I had to design a comparable Butterworth filter, it required
a dynamic range of about 80 dB, and I ended up with the following
precisions in a lattice (ARMA) structure: 22 bit internal data, and 12 
bit coefficients.  This was a 4th order filter with a passband 
of 0.01 * Fs.  The internal data values required four additional
bits to the left of the binary point than did the input value.
This seems (roughly) comparable to what you're trying to do.

As I mentioned, I like to plot RMS error (in dBc) vs. input signal level
(in dB relative to some nominal level) to visualize quantization
effects.  Such a plot should typically have a flat floor in the middle of 
the usable range (representing the limits of your coefficient 
quantization; this includes your stop-band artifacts); it should have a 
6 dB/octave slope in the lower-signal range (resulting from the data-path 
quantization); and a steep saturating effect at high signal levels.  If 
you do not obtain this sort of U-shaped or V-shaped curve, something is 
seriously wrong.  

(I do not think this is one of the plots fdatool likes to spit out on
its own.)


Steve

"Steve Pope" <spope33@speedymail.org> wrote in message 
news:i3n53q$9sq$1@blue.rahul.net...

> Back to the OP's problem -- it occurs to me that if he is intending to
> use fdatool's design path through to HDL generation,

I'd be prepared to use the tool's HDL generation, but assumed
that it probably wouldn't do what I needed. I have a relatively low
sample rate, so I was just going to use a pool of memory and a MAC,
and put all the complexity in the memory control. I can't find
any way of making the Matlab HDL generator do that
(nor did I really expect to).

>  then he is
> probably stuck figuring out how the tool's fixed-point modes work,
> thus making the advice given in this thread of limited value.
>
> (But I would still do a grounds-up quantization study independent of
> the tool even in this case, approaching it as I outlined in
> response to OP's previous question.)

I think I'll have to do that. I just need to get some familiarity with
Matlab first (any paper / text you could recommend on doing a
grounds up quantization study on an IIR?).

It seemed to me that the FDATool pretty much did what I needed,
but as I began to work with it I realized some of the answers I was
getting were counter-intuitive. For relatively wide LPFs, the default
quantization choices seem to be reasonable. The noise analysis
shows about 60 dB stop-band artifacts, but I can increase
accuracy at various points in the filter, and get the performance I need.

It's when I try to understand what the various controls mean that I
get a bit frustrated. The documentation just expands slightly on
the titles of the boxes, but doesn't really explain anything.
For example, the default 6th order Butterworth LPF has an input
of 16-bits with 15 fractional, and an output of 16-bits with 10 fractional.
Why would I need anything more than two bits before the binary
pont on the output? Clearly I don't understand what their
nomenclature means, but I can't find any detailed information (I know
I've repeated myself with a previous question, but I'm hoping
someone on the matlab group might answer).

Things get worse when I go to higher accuracy and narrower filters.
If I start looking at a filter with f3db = 0.05, things get messy. The 
response
is ugly, the stop-band artifacts are extremely high, and the tool does
things I don't expect. It doesn't seem to default to higher accuracy in the
data path for narrower filters, but when I change to higher accuracy the
performance gets much worse. I'm not sure if the tool is broken, I'm
ignorant, or a combination of the two (wierd rendering bugs in the GUI don't
fill me with confidence though.).

I seem to get bad results with any architecture. DF2SOS is weird, but
I tried Steve's earlier suggestion of ARMA, and converted a 6th
order Butterworth LPF with f3db = 0.05 to ARMA. The floating
point response looks fine, but converting to fixed point with the
tool's defaults gives me a Magnitude Response Estimate of about -80 dB
from DC to Nyquist. Doubling the number of bits everywhere gives me
an MRE of -140 dB from DC to Nyquist (note, this is Magnitude
Response Estimate -- not Noise Power Spectrum).

I've also got to decide whether / what I'm buying from Mathworks
(the current system is a loaner). I started off liking its power, but am
now thinking it's either buggy or I'm too stupid to use it.

Thanks

Pete

Richard Owlett  <rowlett@pcnetinc.com> wrote:

>Rick Lyons wrote:

>> I believe the safest thing to do is write your own
>> in-line MATLAB code, that way you know exactly what
>> the code is doing.

>I would like to paraphrase, for benefit of students and other 
>NEWBIES, as:
>'the safest thing to do is write your own {insert tool of choice}
>  code, that way you know exactly what the code is doing. You 
>might also learn why designer made specific choices. Not to 
>mention that you discover holes in your understanding.'

>By expertise I'm a newbie, by age I'm older than most of group ;)

I doubt you're a newbie in any normal sense of the term.

Back to the OP's problem -- it occurs to me that if he is intending to 
use fdatool's design path through to HDL generation, then he is 
probably stuck figuring out how the tool's fixed-point modes work,
thus making the advice given in this thread of limited value.

(But I would still do a grounds-up quantization study independent of 
the tool even in this case, approaching it as I outlined in 
response to OP's previous question.)

Steve