Design and implementation of approximately linear phase two-dimensional IIR filters

A new method for designing separable denominator two-dimensional (2-D) infinite-response response (IIR) digital filters with approximately linear phase in the passband is proposed. This method is based on the model reduction of a linear phase finite-impulse response (FIR) filter using 2-D impulse response Gramians. The implementation of these filters using fixed-point arithmetic is also considered and an algorithm for obtaining a low roundoff noise structure with high computational efficiency is presented. Furthermore, a lower bound for the number of bits required for a 2-D IIR filter implementation with free of overflow oscillations is given. The resulting 2-D IIR digital filter has four advantages: (1) approximately linear phase in the passband; (2) low global roundoff noise; (3) high computational efficiency; and (4) no overflow oscillations under various overflow nonlinearities