Synthesis and Realization of Two-Dimensional Separable Denominator Orthogonal Systems via Decomposition Into 1-D Systems

This paper presents a realization and implements techniques of 2-D linear time-invariant discrete filters described by a system function. Two classes are covered: finite- and infinite-impulse response systems with a separable denominator. This realization is based on a state-space approach, known as orthogonal filters, resulting in structures consisting of Givens rotations and delays. The techniques that are presented are illustrated by an edge detection system and a separable denominator band-pass filter designs. For the designed structures, magnitude errors caused by a finite precision arithmetic have been evaluated and compared with those obtained for direct structures based on difference equations. It has been shown that orthogonal structures possess lower magnitude errors.