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The kernel in Cohen's generalized time frequency representation (GTFR) requires is chosen in accordance to certain desired performance attributes. Properties of the kernel are typically expressed as constraints. We establish that many commonly used constraints are convex in the sense that all allowable kernels satisfying a given constraint form a convex set. Thus, for a given set of constraints, the kernel can be designed by alternately projecting among these sets. If there exists a nonempty intersection among the constraint sets, then the theory of projeciion onto convex seis ( POCS) guarantees convergence to a point in the intersection. If the constraints can be partitioned into two sets, each with a nonempty intersection, then POCS guarantees convergence to a kernel that satisfies the inconsistent constraints with minimum mean square error.
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