Design of Time-Frequency Representations Using a Multiform, Tiltable Exponential Kernel
Document Type
Article
Date of Original Version
1-1-1995
Abstract
A novel Cohen’s class time-frequency representation with a tiltable, generalized 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, diamonds, rectangles, parallel strips at arbitrary angles, crosses, snowflakes, etc., and narrower transition regions than conventional Cohen’s class kernels; this versatility enables the new kernel to suppress undesirable cross terms in a broader variety of time-frequency scenarios. The second advantage of the new kernel is that closed form design equations can now be easily derived to select kernel parameters that meet or exceed a given set of user specified passband and stopband design criteria in the ambiguity function plane. Thirdly, it is shown that simple constraints on the parameters of the new kernel can be used to guarantee many desirable properties of time-frequency representations. The well known Choi-Williams exponential kernel, the generalized exponential kernel, and Nuttall’s tilted Gaussian kernel are special cases of the proposed kernel. © 1995 IEEE
Publication Title, e.g., Journal
IEEE Transactions on Signal Processing
Volume
43
Issue
10
Citation/Publisher Attribution
Costa, Antonio H., and G. F. Boudreaux-Bartels. "Design of Time-Frequency Representations Using a Multiform, Tiltable Exponential Kernel." IEEE Transactions on Signal Processing 43, 10 (1995): 2283-2301. doi: 10.1109/78.469860.