Synthesis of separable‐denominator multidimensional digital lattice filters

Digital filters play an important role in multidimensional signal processing. Because the coefficients must be expressed in finite wordlength, the deterioration of the characteristics becomes a problem. Using a lattice structure whose efficiency has been confirmed for one‐dimensional (1‐D) digital filters, this paper proposes a unified synthesis method for the practically important separable‐denominator multidimensional IIR digital filters. First, the implementation of a 2‐D separable‐denominator transfer function by a separable‐denominator 2‐D digital lattice filter is considered. A characteristic of the proposed separable‐denominator 2‐D digital lattice filter is that both the usual tapped lattice structure and the injection‐type lattice structure are used and the signal flow becomes simple compared to the method so far. Next, when the numerator polynomial is a mirror‐image polynomial, an implementation method is presented in which the number of tap multipliers is reduced significantly. Furthermore, a method is suggested for the synthesis of a 3‐D transfer function based on the same approach as for the 2‐D case. Finally, the efficiency of this method is confirmed by an example.