Algorithmic Design of Realizable Low-Order IIR Filters for Phase Matching

Designing digital filters with desired phase responses at selected frequencies is essential in several communication and control applications. While phase compensation is generally achieved using all-pass filters, the all-pass constraint limits the range of realizable stable, causal filters that match the desired phase characteristics. In this paper, we present a method for designing real, stable discrete-time filters that match phase constraints at selected frequencies. Our approach enables control over the phase response without affecting stability and with low complexity. Specifically, we construct an nth-order filter to match phase constraints at n distinct frequencies (for even n), achieving exact phase interpolation with a low filter order. The derived methodology cascades suitably designed second order sections, referred to as filter blocks, and uses a fixed-point iteration scheme to meet the phase specifications, with tunable design parameters that enable explicit control over the margin of stability. Simulations confirm the utility of our method for obtaining stable filters that satisfy phase specifications even where comparable methods, such as all-pass designs, fail.