Introduction to DSP - IIR filters: parallel and cascade IIR structures

Because IIR filters are very sensitive to quantisationerrors, they are usually implemented as second order sections.

The parallel form is simple:

The outputs from each second order section are simply added together.

If scaling is required, this is done separately for each section. It is possible to scale each section appropriately, and by a different scale factor, to minimise quantisation error. In this case another extra multiplier is required for each section, to scale the individual section outputs back to the same common scale factor before adding them.

The order in which parallel sections are calculated does not matter, since the outputs are simply added together at the end.

In the cascade form, the output of one section forms the input to the next:

Mathematically, it does not matter in which order the sections are placed - the result will be the same. This assumes that there are no errors. In practice, the propagation of errors is crucial to the success of an IIR filter so the order of the sections in the cascade form is vital.