1 November 1990 Kernel synthesis for generalized time-frequency distributions using the method of projections onto convex sets
Author Affiliations +
Abstract
The kernel in Cohen's generalized time frequency representation (GTFR) requires is chosen in accordance to certain desired performance attributes. Properties of the kernel are typically expressed as constraints. We establish that many commonly used constraints are convex in the sense that all allowable kernels satisfying a given constraint form a convex set. Thus, for a given set of constraints, the kernel can be designed by alternately projecting among these sets. If there exists a nonempty intersection among the constraint sets, then the theory of projeciion onto convex seis ( POCS) guarantees convergence to a point in the intersection. If the constraints can be partitioned into two sets, each with a nonempty intersection, then POCS guarantees convergence to a kernel that satisfies the inconsistent constraints with minimum mean square error.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Seho Oh, Robert Jackson Marks, Les E. Atlas, James W. Pitton, "Kernel synthesis for generalized time-frequency distributions using the method of projections onto convex sets", Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); doi: 10.1117/12.23477; https://doi.org/10.1117/12.23477
PROCEEDINGS
11 PAGES


SHARE
RELATED CONTENT

Signal arrival times
Proceedings of SPIE (December 24 2003)
Wavelet-based technique for detection of mechanical chaos
Proceedings of SPIE (April 05 2000)
Chirp correlation in the wavelet domain
Proceedings of SPIE (December 22 1997)
Construction of time-frequency representations from moments
Proceedings of SPIE (September 25 2007)

Back to Top