# Basic theory of IIR filters

**URL:** <https://www.ruby-forum.com/t/basic-theory-of-iir-filters/242055>\
**Category:** GNU Radio\
**Created:** [May 22, 2015, 9:21pm UTC](https://www.ruby-forum.com/t/basic-theory-of-iir-filters/242055 "2015-05-22T21:21:30Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Detlef\_R](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/d/58f4c7/32.png) [@Detlef\_R](https://www.ruby-forum.com/u/Detlef_R)\
**Post date:** [May 22, 2015, 9:21pm UTC](https://www.ruby-forum.com/t/basic-theory-of-iir-filters/242055/1 "2015-05-22T21:21:30Z")

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I’ve switch back with filters, and I’d like to implement a IIR  
filters,also  
because I’ve seen that there are different papers about IIR filters in  
CUDA,but I didn’t see any implementation.

I’ve see that actually gnuradio is using a direct form I  
implementation,which cannot be easily ported.

So I’ve looked about cascade and parallel FIR filter. My question is:  
which  
is best in terms of stability?Is acceptable to decompose the transfer  
function in sub-function with only one pole?or could it cause  
instability?(e.g. conjugate poles).  
Otherwise,due to the fact that both approaches(parallel and cascade)  
require only the previous output,I think what the implementaion would be  
not difficult: thanks to the expansion of recurrence expression, is  
“sufficient” something like a parallel sum prefix.

Thanks,  
Marco Ribero