Mixed-norm fir filter optimization using second-order cone programming

It has been shown that second-order cone programming (SOCP) can be used to efficiently optimize FIR filter frequency responses in the sense of L1, L2, and L∞. Although SOCP cannot be used for the more general case of Lp minimization, several techniques for combining norms provide the flexibility to minimize a continuum of norms from L1 to L∞. Burdakov´s vector ε-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 in the examples.