Design of inherently stable two-dimensional recursive filters imitating the behaviour of one-dimensional analog filters

A novel method is presented for the design of two-dimensional (2-D) recursive filters that are inherently stable, thereby avoiding computationally lengthy tests of stability. The new method is based on mapping the 1-D continuous complex frequency variable s by an appropriate function of the 2-D digital filter variables Z1and Z2. Thus, passive analog filters (Butterworth, Chebyshev or Cauer) may readily be transformed into the 2-D digital domain, preserving certain desirable aspects of the 1-D characteristics, as well as avoiding the cumbersome computations required to synthesize stable two-variable transfer functions. Some examples are presented to demonstrate the excellent response, e.g. circular symmetry, obtained using the new technique. The advantages of this approach over other methods suggested for stable 2-D recursive filter design, are briefly discussed.