DESIGN OF TIME-FREQUENCY REPRESENTATIONS USING A MULTIFORM, TILTABLE EXPONENTIAL KERNEL

A novel Cohen's class time-frequency representation with a tiltable, g eneralized exponential kernel capable of attaining a wide diversity of shapes in the ambiguity function plane is proposed for improving the time-frequency analysis of multicomponent signals, The first advantage of the proposed kernel is its ability to generate a wider variety of passband shapes, e.g., rotated ellipses, generalized hyperbolas, diamo nds, rectangles, parallel strips at arbitrary angles, crosses, snowfla kes, etc, and narrower transition regions than conventional Cohen's cl ass kernels; this versatility enables the new kernel to suppress undes irable cross terms in a broader variety of time-frequency scenarios, T he second advantage of the new kernel is that closed form design equat ions can now be easily derived to select kernel parameters that meet o r exceed a given set of user specified passband and stopband design cr iteria in the ambiguity function plane, Thirdly, it is shown that simp le constraints on the parameters of the new kernel can be used to guar antee many desirable properties of time-frequency representations. The well known Choi-Williams exponential kernel, the generalized exponent ial kernel, and Nuttall's tilted Gaussian kernel are special eases of the proposed kernel.