Time-frequency kernel design via point and derivative constraints

Point and derivative constraints are used to provide a wide class of kernels suitable for time-frequency representation of signals. The kernel design is viewed as a solution of linearly constrained minimization problem 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 beamforming, where the Quiescent pattern corresponds to the Born-Jordan kernel. The constraint matrix can be augmented by derivative constraints which extend the solution space to include kernels with various characteristics