Design of an Optimal Two-Channel Orthogonal Cyclic Filterbank Using Semidefinite Programming

A simple method for the design of an optimal two-channel orthogonal cyclic filterbank using semidefinite programming is presented. The criterion for optimality is to maximize the passband energy, or equivalently, to minimize the stopband energy of the filter's impulse response. The objective function and orthogonality constraints are represented in terms of the cyclic autocorrelation sequence of the filter's impulse response. The convex formulation of the filter design problem is obtained by imposing the positive semidefinite property on the cyclic autocorrelation matrix. The solution of the semidefinite programming problem gives a class of optimal cyclic filters with unique discrete Fourier transform magnitude response. The design method is illustrated with an example.