Mixed H2/H∞ design of non-uniform filter banks using an efficient realisation of synthesis stage

In this paper we address the problem of designing a nonuniform filter bank (NUFB) using a mixed H₂/H_∞ optimisation. The solution to H_∞ optimisation for minimising the worst case error norm is not unique. Hence we optimise with respect to an additional H₂ criterion. It results in a mixed H₂/H_∞ optimisation problem. We formulate the optimisation problem as a linear matrix inequality (LMI). To remove the structural dependencies in the synthesis stage and to achieve low circuit layout complexity, we design an efficient synthesis stage. We perform simulations using the LMI tool-box in MATLAB to validate the theory.