The application of dynamic programming to the optimal ordering of digital filter sections

Dynamic Programming has been applied to a number of digital signal processing problems. In this paper we discuss its well known application to the problem of determining the optimum order of sections in a digital filter realization. We show that the method is quite insensitive to the specific details of the problem; it is applicable over a wide range of possible optimality criteria, various kinds of arithmetic, scaling options, etc. This is characteristic of the application of dynamic programming to many signal processing problems. Also, since a problem, to be solved by dynamic programming, must be represented as the traversal of a directed graph, we usually discover unsuspected structure in the problem when we attempt to solve it using dynamic programming. Quite often it is necessary to recognize this structure in order to solve the problem efficiently. In the case of ordering of filter sections the structure leads to an efficient utilization of memory.