Classical IIR filter problem

Hi,

I had designed a digital IIR filter from the existing analog
prototype. The filter coefficients were obtained using MATLAB. The DSP
which is used here is the TMS320F2812 processor. The problem is
scaling of filter coefficients.The input data length to the filter is
12 bits. I had scaled the filter coeffiecients to 9 bits. But then
with these available datalengths,its difficult to predict the no. of
output bits as the filter is recursive. Two filters have been
implemented. One is a second order filter amd the other one is a
fourth order filter. I know that these quantization errors are non
linear and its very difficult to predict the error. But whats the work
around? Shd I use trial and error method to find out the exact scaling
for my filter coefficients or any other better way exists? Any help in
this regards would be greatly appreciated.

Regards,
Kalyani

kalki wrote:
> Hi,
>=20
> I had designed a digital IIR filter from the existing analog
> prototype. The filter coefficients were obtained using MATLAB. The DSP
> which is used here is the TMS320F2812 processor. The problem is
> scaling of filter coefficients.The input data length to the filter is
> 12 bits. I had scaled the filter coeffiecients to 9 bits. But then
> with these available datalengths,its difficult to predict the no. of
> output bits as the filter is recursive. Two filters have been
> implemented. One is a second order filter amd the other one is a
> fourth order filter. I know that these quantization errors are non
> linear and its very difficult to predict the error. But whats the work
> around? Shd I use trial and error method to find out the exact scaling
> for my filter coefficients or any other better way exists? Any help in
> this regards would be greatly appreciated.
>=20
> Regards,
> Kalyani

The TMS320F2812 supports 32 bit MAC so

1. use the full width of the available words, 32 bit, (but 16 bit=20
coefficients should do for 12 bit data)

2. split your filter in second order sections (may be done in Matlab)

Ren=E9

Ren� wrote:
> kalki wrote:
> 
>> Hi,
>>
>> I had designed a digital IIR filter from the existing analog
>> prototype. The filter coefficients were obtained using MATLAB. The DSP
>> which is used here is the TMS320F2812 processor. The problem is
>> scaling of filter coefficients.The input data length to the filter is
>> 12 bits. I had scaled the filter coeffiecients to 9 bits. But then
>> with these available datalengths,its difficult to predict the no. of
>> output bits as the filter is recursive. Two filters have been
>> implemented. One is a second order filter amd the other one is a
>> fourth order filter. I know that these quantization errors are non
>> linear and its very difficult to predict the error. But whats the work
>> around? Shd I use trial and error method to find out the exact scaling
>> for my filter coefficients or any other better way exists? Any help in
>> this regards would be greatly appreciated.
>>
>> Regards,
>> Kalyani
> 
> 
> The TMS320F2812 supports 32 bit MAC so
> 
> 1. use the full width of the available words, 32 bit, (but 16 bit 
> coefficients should do for 12 bit data)
> 
> 2. split your filter in second order sections (may be done in Matlab)
> 
> Ren�
> 

There's two things you need to look at:  One is the quantization noise 
from the on-going arithmetic, the other is the loss of precision of the 
filter weights as you increase the polynomial order.

I estimate quantization noise in my IIR filters by finding the transfer 
function from each summation to the output, and assuming noise at 2x to 
4x the lsb.  If the output noise is too great I adjust things.  This is 
why Ren� is suggesting 32-bit data (although on the '2812 you're forced 
into 32-bit coefficients when you use 32-bit data so you may as well go 
there).

Both the coefficient precision and quantization noise go up as your 
filter poles approach z = 1.  Basically you need enough precision to 
resolve the difference between your transfer function and (z - 1)^n. 
For example, a 2nd-order filter with poles at z = 0.99 needs to have 
enough precision to resolve the difference between 0.9801 and 0.9800, or 
(0.01)^2.  With a 4th-order filter you'd need (0.01)^4.  To make sure 
you should calculate your filter coefficients, round them, then check 
actual transfer function of the algorithm with the rounded coefficients. 
  Here again using 32-bit coefficients relaxes your requirements for you.

One final note:  Pay attention to scaling.  I run transfer function 
plots of all the state variables of my filters, looking for peaks above 
magnitude 1.  Then I ask myself if I'm going to get enough excitation at 
that frequency to saturate my variables, and I think about scaling my 
inputs and outputs.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:107td4f4ig31maa@corp.supernews.com...
> Ren&#4294967295; wrote:
> > kalki wrote:
> >
> >> Hi,
> >>
> >> I had designed a digital IIR filter from the existing analog
> >> prototype. The filter coefficients were obtained using MATLAB. The DSP
> >> which is used here is the TMS320F2812 processor. The problem is
> >> scaling of filter coefficients.The input data length to the filter is
> >> 12 bits. I had scaled the filter coeffiecients to 9 bits. But then
> >> with these available datalengths,its difficult to predict the no. of
> >> output bits as the filter is recursive. Two filters have been
> >> implemented. One is a second order filter amd the other one is a
> >> fourth order filter. I know that these quantization errors are non
> >> linear and its very difficult to predict the error. But whats the work
> >> around? Shd I use trial and error method to find out the exact scaling
> >> for my filter coefficients or any other better way exists? Any help in
> >> this regards would be greatly appreciated.
> >>
> >> Regards,
> >> Kalyani
>
> One final note:  Pay attention to scaling.  I run transfer function
> plots of all the state variables of my filters, looking for peaks above
> magnitude 1.  Then I ask myself if I'm going to get enough excitation at
> that frequency to saturate my variables, and I think about scaling my
> inputs and outputs.

Good advice.  Another option is to switch to a different filter topology that
has better characteristics in terms of state variable magnitude, e.g. normalized
lattice/ladder.  Me, I am fortunate enough to be working primarily with 32- or
40-bit floating-point DSPs where this is much less of an issue!

Typically when doing IIR in fixed point environment you'll want to break it
into second order stages (as suggested).  When doing this there is a good
chance that one of the coefs will be greater than 1.0 and typically the
coefs are represented as 16 bit Q15 values whos represented range is +/-1.
The work around for this normally involves dividing that coeficient in half
and adding that coef*y() product twice to a 32 bit accumulator.

Check TI's web site they've got any DSP support for 28x:

http://dspvillage.ti.com/docs/catalog/devtools/dsptoolslist.jhtml?familyId=110&toolTypeId=44&toolTypeFlagId=1&ptemplateId=5121&pnavigationId=9110

-Shawn Steenhagen
www.appliedsignalprocessing.com



"kalki" <kalyanik@myw.ltindia.com> wrote in message
news:a130dc51.0404150227.53fd1b7f@posting.google.com...
> Hi,
>
> I had designed a digital IIR filter from the existing analog
> prototype. The filter coefficients were obtained using MATLAB. The DSP
> which is used here is the TMS320F2812 processor. The problem is
> scaling of filter coefficients.The input data length to the filter is
> 12 bits. I had scaled the filter coeffiecients to 9 bits. But then
> with these available datalengths,its difficult to predict the no. of
> output bits as the filter is recursive. Two filters have been
> implemented. One is a second order filter amd the other one is a
> fourth order filter. I know that these quantization errors are non
> linear and its very difficult to predict the error. But whats the work
> around? Shd I use trial and error method to find out the exact scaling
> for my filter coefficients or any other better way exists? Any help in
> this regards would be greatly appreciated.
>
> Regards,
> Kalyani

Hi

I know they don't have a student version (I'm presuming that you are a
student),
but if you can get your hands on ONEoverT, it will generate your
floating point coefficients and their fixed point equivalents. You can
specify the input and output number of bits and then see what the
result will be like. It's a great program and doesn't come near the
price of other overpriced counterparts.

Bob

kalyanik@myw.ltindia.com (kalki) wrote in message news:<a130dc51.0404150227.53fd1b7f@posting.google.com>...
> Hi,
> 
> I had designed a digital IIR filter from the existing analog
> prototype. The filter coefficients were obtained using MATLAB. The DSP
> which is used here is the TMS320F2812 processor. The problem is
> scaling of filter coefficients.The input data length to the filter is
> 12 bits. I had scaled the filter coeffiecients to 9 bits. But then
> with these available datalengths,its difficult to predict the no. of
> output bits as the filter is recursive. Two filters have been
> implemented. One is a second order filter amd the other one is a
> fourth order filter. I know that these quantization errors are non
> linear and its very difficult to predict the error. But whats the work
> around? Shd I use trial and error method to find out the exact scaling
> for my filter coefficients or any other better way exists? Any help in
> this regards would be greatly appreciated.
> 
> Regards,
> Kalyani