A unified approach to the design of 2-D IIR digital filters with flat passband magnitude and delay characteristics

In this paper we present a unified procedure to the design of 2-D IIR filters with flat passband characteristics in both magnitude and delay. We first propose an analytical procedure to design maximally flat delay 1-D IIR filters with flat passband and flat/equiripple stopband magnitude characteristics. We then present a Digital Spectral Transformation (DST) to obtain stable 2-D IIR transfer functions by transforming a stable 1-D prototype. The few parameters of the DST are found using a simple optimization technique such that the 3-dB bandwidth of the 1-D prototype maps to the desired contour in the ω₁ -ω₂ plane. In this unified method no computationally expensive non-linear optimization techniques are employed, the 2-D filter is guaranteed to be stable, the error between the specified passband contour and the actual passband contour is very small and the flat passband characteristics in both magnitude and delay response of the 1-D prototype filter is well preserved by the 2-D filter