Converting IIR filters to parallel form

This is the companion page of the paper

Balázs Bank, "Converting Infinite Impulse Response Filters to Parallel Form", (Also available at IEEEXplore) IEEE Signal Processing Magazine, Vol. 35, Iss. 3, pp. 124-130, May 2018.

Companion page address:


Discrete-time rational transfer functions are often converted to parallel second-order sections due to better numerical performance compared to direct form IIR implementations. This is usually done by performing partial fraction expansion over the original transfer function. When the order of the numerator polynomial is greater or equal to that of the denominator, polynomial long division is applied before partial fraction expansion resulting in a parallel FIR path. This paper shows that applying this common procedure can cause a severe dynamic range limitation in the filter because the individual responses can be much larger than the net transfer function. This can be avoided by applying a delayed parallel form where the response of the second-order sections is delayed in such a way that there is no overlap between the IIR and FIR parts. In addition, a simple least-squares procedure is presented to perform the conversion which is numerically more robust than the usual Heaviside partial fraction expansion. Finally, the possibilities of converting series second-order sections to the delayed parallel form are discussed.

Fig. 1: the structure of the delayed parallel filter.


Here you can find the Matlab code to reproduce the figures of the paper and all the functions needed for converting IIR filters to the delayed parallel second-order form. (all files as a zip file)

Here are the most important commands required for converting a direct-form B(z)/A(z) filter or a series second-order structure to the delayed parallel form:

Some auxiliary files required to run the codes creating the figures:

You can find more info about fixed-pole parallel filters here and you may also want to check my entire list of publications.

(c) Balazs Bank, 2018. All rights of the codes reserved to the author. Non-commercial use permitted, for all other uses, please contact the author.

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Last modified: 30.01.2018.