Design of three‐dimensional separable‐denominator digital filters via singular‐value decomposition
Takao Hinamoto, Takashi Hamanaka, Sadao Maekawa · Electronics and Communications in Japan (Part I Communications) · 1988
Abstract This paper considers the situation in which the desired three‐dimensional impulse response is represented as a finite series, and discusses the spatial domain design of the three‐dimensional recursive digital filter, which approximates the desired response by a separable‐denominator three‐dimensional local state‐space model. As the first step, a necessary and sufficient condition is derived for the separable‐denominator three‐dimensional local state‐space model to be separately locally controllable and separately locally observable. It is shown that the condition is equivalent to the minimality of three one‐dimensional systems. Then the given three‐dimensional impulse response is represented formally in terms of three one‐dimensional impulse responses, and the coefficients of the separable‐denominator local state‐space model are designed through the singular‐value decomposition of the Hankel matrices. Finally, the validity of the proposed method is verified by a numerical example.