Parallel realization method for multidimensional digital filters

This paper proposes a new method for approximately decomposing the general form multi-dimensional (M-D) digital filters into the combination of parallel sections which are composed of cascaded one-dimensional (1-D) digital filters with different delay elements. At first, the coefficients of M-D filters are used to construct a M-D coefficient array. Then a new technique is proposed to decompose the M-D coefficient array into the summation of the outer products of several real-valued vectors. Since the real-valued vectors represent the coefficients of 1-D filters with different delay elements, the above decomposition of the M-D coefficient array implies that a general M-D digital filter can be approximately decomposed into the combination of totally parallel sections, and each section is composed of cascaded 1-D filters. Consequently, the structure of the realized M-D filter possesses high parallelism, regularity and modularity, it is suitable for high speed parallel signal processing and VLSI implementation.