Design of 2-D linear phase IIR digital filters using 2-D impulse response gramians and implementation with low roundoff noise and no overflow oscillations

A new method for designing separable denominator 2-D IIR digital filters with linear phase in the passband is proposed. This method is based on the model reduction of a linear phase 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. The resulting 2-D IIR digital filter has four advantages: (i), linear phase characteristics; (ii), low global roundoff noise; (iii), high computational efficiency; (iv), and no overflow oscillations (limit-cycle free) under the saturation overflow nonlinearity.