IIRFIR

IIRFIR is a term used in digital signal processing to describe a hybrid filter architecture that combines Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) components in a single system. The aim is to leverage the strengths of both families: the IIR part can realize sharp magnitude responses with relatively low order, while the FIR part provides linear phase characteristics and precise control over the impulse response.

Common realizations include cascaded designs where an IIR section is followed or preceded by an FIR stage, and parallel configurations in which the input is split and processed by different filter types before recombination. The combination can be tailored to meet specific spectral and phase requirements, with design choices around where to place the IIR and FIR elements, how to manage delays, and how to compensate phase distortion.

Key design considerations include stability of the IIR portion, phase linearity, group delay, and sensitivity to coefficient quantization. Numerical precision and round-off can affect both stability and performance, particularly in fixed-point implementations. Hybrid structures may employ techniques such as state-space realizations, pole-zero placement in the IIR part, and FIR pre- or post-filtering to shape or linearize the overall response.

Applications span audio processing, adaptive and fixed filtering in communications receivers, digital equalization, and anti-imaging or anti-aliasing in sample-rate conversion. While IIRFIR designs can offer efficiency and flexible phase control, they require careful analysis to ensure stability and predictable behavior across operating conditions.