Second-Order Cone Formulations of Mixed-Norm Error Constraints for FIR Filter Optimization
Dan P. Scholnik, J.O. Coleman · 2010
Abstract : It has been previously shown that second-order cone programming (SOCP) can be used to efficiently optimize FIR filter frequency responses in the sense of L1, L2, and Linf. Although SOCP cannot be used for the more general case of Lp minimization, two techniques for combining norms provide the flexibility to minimize a continuum of norms from L1 to Linf. The recently introduced vector epsilon-norm is here extended to complex functions on an interval of the real line, and is compared with a simple convex combination of norms. The dual norms of both are found as well. Discretized approximations of these norms can be used for filter design with SOCP, as shown by several examples.