merging FIR filter with feedforward IIR coeffecients?

Hello
I have a 7 tap FIR which performs sinx compensation. This is followed by a
second order IIR group delay equalisation which corrects the D/A
reconstruction filters response. I am tight on space in my DSP so want to
know if it is possible to remove the 3 feedforward coeffecients from the IIR
section and combine them into the 7 TAP fir inverse sinx filter
Thanks in advance for any tips and pointers.

On Wed, 13 Oct 2004 22:07:27 GMT, "scott"
<scott@SPAMOFFbroadcastwarehouse.com> wrote:

>Hello
>I have a 7 tap FIR which performs sinx compensation. This is followed by a
>second order IIR group delay equalisation which corrects the D/A
>reconstruction filters response. I am tight on space in my DSP so want to
>know if it is possible to remove the 3 feedforward coeffecients from the IIR
>section and combine them into the 7 TAP fir inverse sinx filter
>Thanks in advance for any tips and pointers.
>

Hi Scott,

  off hand, I don't think you can remove the 3 feedforward 
coeffecients from the IIR section and combine them with 
the 7 TAP FIR filter.

When the two filters are cascaded, the "combined" 
transfer function in the z-domain will be a ratio 
whose numerator is the product of the numerator 
polynomial of the IIR filter and the FIR filter.
So that "combined" ratio's numerator polynomial will 
be higher in order than the FIR filter's 
polynomial.  I guess it's possible that some of the 
terms in the combined ratio's numerator polynomial 
end up being zero, but I can't say.

Maybe the other guys here will have a useful idea, 
or two, for you.

Good Luck,
[-Rick-]

Rick Lyons wrote:

> On Wed, 13 Oct 2004 22:07:27 GMT, "scott"
> <scott@SPAMOFFbroadcastwarehouse.com> wrote:
> 
>>Hello
>>I have a 7 tap FIR which performs sinx compensation. This is
>>followed by a second order IIR group delay equalisation which
>>corrects the D/A reconstruction filters response. I am tight on
>>space in my DSP so want to know if it is possible to remove the
>>3 feedforward coeffecients from the IIR section and combine them
>>into the 7 TAP fir inverse sinx filter Thanks in advance for any
>>tips and pointers. 
>>
> 
> Hi Scott,
> 
>   off hand, I don't think you can remove the 3 feedforward 
> coeffecients from the IIR section and combine them with 
> the 7 TAP FIR filter.
> 
> When the two filters are cascaded, the "combined" 
> transfer function in the z-domain will be a ratio 
> whose numerator is the product of the numerator 
> polynomial of the IIR filter and the FIR filter.
> So that "combined" ratio's numerator polynomial will 
> be higher in order than the FIR filter's 
> polynomial.  I guess it's possible that some of the 
> terms in the combined ratio's numerator polynomial 
> end up being zero, but I can't say.

I don't think Scott meant to imply that the order of the combined 
filter should stay 7, so the theoretical answer would be yes: you can 
convolve the numerator coefficient sequence with the FIR sequence 
for a result of length 9. But what that will do to the numerics of 
the overall system I don't know.


Martin

-- 
Quidquid latine dictum sit, altum viditur.