Forums

IIR on TI 55xx

Started by AntonZ July 23, 2003
I try to implement an IIR on a 16-bit fixed-point 5510 DSP. After
calculating the filter in Matlab, I got the following coefficients:

>> iir.tf.num
ans = 1.0e-005 * 0.0868 0.3470 0.5205 0.3470 0.0868
>> iir.tf.den
ans = 1.0000 -3.8373 5.5250 -3.5375 0.8498 Now I decompose the filter into two biqads:
>> tf2sos(iir.tf.num,iir.tf.den)
ans = 0.0000 0.0000 0.0000 1.0000 -1.8876 0.8913 1.0000 2.0000 1.0000 1.0000 -1.9497 0.9535 Exellent. Now I want to use DSPLib's iircas5 to implement the filter. The problem is that DSPLib needs coefficients in Q.15, while there are some coefficients that are impossible to fit in Q.15 number. I don't know what should I do, how can I use the calculated filter with the DSPLib procedures? Thanks, Anton Zemlyanov
anton@global-ops.com (AntonZ) wrote:

>I try to implement an IIR on a 16-bit fixed-point 5510 DSP. After >calculating the filter in Matlab, I got the following coefficients: > >>> iir.tf.num > >ans = > > 1.0e-005 * > > 0.0868 0.3470 0.5205 0.3470 0.0868 > >>> iir.tf.den > >ans = > > 1.0000 -3.8373 5.5250 -3.5375 0.8498 > >Now I decompose the filter into two biqads: > >>> tf2sos(iir.tf.num,iir.tf.den) > >ans = > > 0.0000 0.0000 0.0000 1.0000 -1.8876 0.8913 > 1.0000 2.0000 1.0000 1.0000 -1.9497 0.9535 > >Exellent. Now I want to use DSPLib's iircas5 to implement the filter. >The problem is that DSPLib needs coefficients in Q.15, while there are >some coefficients that are impossible to fit in Q.15 number. I don't >know what should I do, how can I use the calculated filter with the >DSPLib procedures?
Divide them by the power of two that makes them all less than one in absolute magnitude. Multiply the resulting numbers by 32768. Round to the nearest integer. That's your coefficients. Take the pre-divide out after the filter multiplication and additions, using shifts. Robert www.gldsp.com ( modify address for return email ) www.numbersusa.com www.americanpatrol.com
Thanks a lot Robert!

r_obert@REMOVE_THIS.hotmail.com wrote in message news:<7lu2iv8sfe3fb9t0dv9dr0resudjkue6sn@4ax.com>...
> Divide them by the power of two that makes them all less than one in > absolute magnitude. Multiply the resulting numbers by 32768. Round > to the nearest integer. That's your coefficients. Take the > pre-divide out after the filter multiplication and additions, using > shifts. > > Robert > > www.gldsp.com > > ( modify address for return email ) > > www.numbersusa.com > www.americanpatrol.com
Dear all,

I have exactly the same problem as Anton, but I'm not clear how the
suggested solution will work correctly (no disrespect intended to Robert).

For a single stage biquad (for simplicity), we have:

w(n) = x(n) - a1*w(n-1) - a2*w(n-2)
y(n) = b0*w(n) + b1*w(n-1) + b2*w(n-2)

In Anton's example (for his second stage), the coefficients are:

a0 = 1
a1 = -1.9497
a2 = 0.9535

b0 = 1
b1 = 2
b2 = 1

(Matlab outputs the coefficients in the order b0, b1, b2, a0, a1, a2)

I see immediately how one can scale the 'b' coefficients at will, and
rescale the output, because each 'b' coefficient acts on w(n), w(n-1) and
w(n-2) to yield y(n).

However, the iircas5 function only accepts a1 and a2 (a0 is implicitly
equal to 1). Therefore, dividing the 'a' coefficients by a factor of 2 (in
this case) will alter the filter characteristics. The coefficients would
then be:

a0 = 1 (implicit)
a1 = -0.9748
a2 = 0.4767

As the 'a' coefficients are applied recursively, dividing a1 and a2 by a
factor of 2 would essentially be dividing the three terms in my first
equation by 1, 2 and 4.

Hopefully I have explained that reasonably clearly, and having banged my
head against this particular problem for a day or two, someone can point
out the error in my logic, or explain how one uses iircas5 under these
circumstances!

Many thanks in advance,

John Sumner

>Thanks a lot Robert! > >r_obert@REMOVE_THIS.hotmail.com wrote in message
news:<7lu2iv8sfe3fb9t0dv9dr0resudjkue6sn@4ax.com>...
>> Divide them by the power of two that makes them all less than one in >> absolute magnitude. Multiply the resulting numbers by 32768. Round >> to the nearest integer. That's your coefficients. Take the >> pre-divide out after the filter multiplication and additions, using >> shifts. >> >> Robert >> >> www.gldsp.com >> >> ( modify address for return email ) >> >> www.numbersusa.com >> www.americanpatrol.com >