Least p/sup th/ power design of complex FIR 2-D filters using the complex Newton method

Abstract

A design of 2-D complex FIR filters is proposed by minimizing the p/sup th/ power norm used to measure the deviation of the FIR filter response from a desired filter response. The solution of this problem cannot be obtained in closed form except for p=2; for arbitrary p>2 the authors present an approach which treats the problem from a complex variable point of view. An iterative scheme is described based on the complex Newton method to find the solution. It has the feature that, starting with p=2, the value of p is increased after each iteration. Because the objective function is convex any local extremum is the global minimum. Convergence can be attained after a moderate number of iterations. A characterization theorem for factorization of 2-D FIR filters in terms of 1D filters is derived. This has strong implications for large order 2-D filter design. Two filter design examples are included.