Electronics and Communications in Japan, Part 3, Vol. 77, No. 3, 1994 zyxwv Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. 76-A, No. I I, November zyxwvu 1993, pp. 1522-1528 Synthesis of Separable-Denominator Multidimensional Digital Lattice Filters Eiji Watanabe, Member Faculty of Systems Engineering, Shibaura Institute of Technology, Omiya, Japan 330 Akinori Nishihara, Member Faculty of Engineering, Tokyo Institute of Technology, Tokyo, Japan 152 SUMMARY Digital filters play zyxwvuts an important role in multidimen- sional signal processing. Because the coefficients must be expressed in finite wordlength, the deterioration of the characteristics becomes a problem. Using a lattice struc- ture whose efficiency has been confirmed for onedimen- sional (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- denominatortransfer function by a separabledenominator 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 zyxwvu so far. Next, when the numerator polynomial is a mirror- image polynomial, an implementation method is present- ed 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. 97 Key words: Multidimensional digital filters; multi- dimensional signal processing; digital lattice filters; digital filters. 1. Introduction With the widespread introduction of digital sys- tems, together with the development of signal processing techniques in both software and hardware, digital pro- cessing of two-dimensional (2-D) signals such as normal and radar images also is becoming popular. With the advent of LSI technology, fast computing devices with large memories were developed and the digital process- ing of 3-D signals which contain an enormous amount of data such as moving images and computer tomography is becoming possible. The central role in such digital signal processing is played by digital filters and, from now on, low cost, small size, and high precision will be more and more required. In digital filters, multiplier coefficients are limited to the finite wordlength and the filter characteristics degrade. Therefore, realization circuits which allow less degradation are desirable in the implementation stage. As low-sensitivity, one-dimensional digital filters which meet ISSN 1042-0967/94/0003-0097 zy @ 1994 Scripta Technica, Inc.