A linearly constrained minimization approach for time-frequency kernel design

This paper introduces a new approach for time-frequency distribution kernel design. In this approach, the desired time-frequency properties are obtained as a solution of linearly constrained minimization problem. The problem is presented in a matrix form in which the desired t-f linear constraints constitute a constraint matrix and the time-frequency kernel is one dimensional. This formulation permits a closed form solution, similar to that encountered in beam forming, where the Quiescent pattern corresponds to the Born-Jordan kernel. The constraint matrix can be augmented by other point and derivative constraints which extend the solution space to include kernels with various characteristics