Time-frequency filtering and synthesis from convex projections

Langford B. White

doi:10.1117/12.23473

1 November 1990 Time-frequency filtering and synthesis from convex projections

Langford B. White

Proceedings Volume 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations; (1990) https://doi.org/10.1117/12.23473
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the boundary of a closed convex subset of L2(R2). This result is obtained by considering the convex set of states on the Heisenberg group of which the ambiguity functions form the extreme points. The form of the projection onto the set of WVDs is deduced. Various linear and non-linear filtering operations are incorporated by formulation as convex projections. An example algorithm for simultaneous time-frequency filtering and synthesis is suggested.

Citation Download Citation

Langford B. White "Time-frequency filtering and synthesis from convex projections", Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); https://doi.org/10.1117/12.23473

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