Time-frequency representations with multiform, tiltable Chebyshev kernels

We formulate and provide design equations for novel time-frequency representations (TFRs) with multiform, tiltable (MT) Chebyshev kernels whose passband support regions are capable of attaining a wide diversity of iso-contour shapes in the ambiguity function (AF) plane, e.g., parallel strips, crosses, tilted and untilted ellipses, diamonds, hyperbolas, rectangles, etc. Simple constraints on the parameters of the new kernels can be used to guarantee many desirable properties of TFRs.