Improving the Manry-Aggarwal Method for Designing Multi-Dimensional FIR Digital Filters,

摘要

M. T. Manry and J. K. Aggarwal recently described an algorithm for use in the design of multi-dimensional FIR digital filters by phase correction. As they observe, their method can be viewed as the steepest descent method for minimizing a certain function f(x): given an approximate solution x(n), a new approaximation is x(n + 1) =x(n) + t(n)p(n) where p(n) = grad f(x(n)) and t(n) is chosen by a simple rule. The authors derive here an improved rule for determining t(n) and an improved direction p(n) (essentially the Fletcher-Reeves conjugate-gradient direction). The resulting method appears to be two to three times as fast as the Manry-Aggarwal method; the additional cost is primarily in storage which roughly doubles. (Author)