Design of an optimal two-channel orthogonal filterbank using semidefinite programming

A simple method for the design of an optimal two-channel finite impulse response (FIR) orthogonal filterbank that minimizes the stopband energy of the filter's impulse response using semidefinite programming (SDP) is presented. The convex formulation is obtained by representing the optimality criterion and the orthogonality constraints in terms of the autocorrelation sequence of the filter's impulse response and mapping them into the SDP framework. The resulting solution is equivalent to the solution obtained by the more complex analytical method.