Design of time-frequency representations using multiform, tiltable kernels

The problem addressed in this paper is that of formulating novel Cohen´s class time-frequency representations (TFRs) with multiform, tiltable kernels capable of attaining a wide diversity of shapes in the ambiguity function (AF) plane, e.g., parallel strips, crosses, tilted and untilted ellipses, diamonds, hyperbolas, rectangles, etc. We derive closed form design equations for an exponential or Butterworth prototype kernel whose parameters meet or exceed the given user specified passband and stopband criteria in the AF plane. Furthermore, simple constraints on the parameters of the new kernels can be used to guarantee many desirable properties of the TFRs