An exact realization of 2-D IIR filters using separable 1-D modules

A method for exact realization of 2-D digital IIR (infinite impulse response) filters using separable 1-D modules is presented. The proposed design utilizes a theorem on separability of multivariable polynomials for writing a 2-D polynomial as the sum of the products of 1-D polynomials of successively reducing orders. Compared to previous separable methods based on singular value decomposition and Jordan form decomposition, the approach has reduced hardware complexity for filter implementation. It is also shown that the method has the same complexity as the lower-upper matrix-decomposition-based method. However, unlike the decomposition-based methods, the filter coefficients are found directly from the impulse response matrices by simple numerically reliable mathematical operations.<>