Optimum Signals and the Uncertainty Principle

Abstract : The problem of finding an optimal signal g(t) which satisfies certain constraints in both the time and frequency domains is examined. Relying on the theory of entire functions, a general representation of g(t) in terms of prolate spheroidal wave functions is obtained which reduces the problem to the solution of a nonlinear integral equation. Particular examples illustrating the solution procedure are discussed. (Author)