JSM 2004 - Toronto

Abstract #301552

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Activity Number: 161
Type: Contributed
Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #301552
Title: G(lambda)-stationary Processes and Their Application to Wave Match Filtering
Author(s): Huiping Jiang*+ and Henry Gray and Wayne A. Woodward
Companies: New York State Psychiatric Institute and Southern Methodist University and Southern Methodist University
Address: 1051 Riverside Rd. #48, New York, NY, 10032,
Keywords: G(lambda)-stationary processes ; filtering ; time-varying frequencies ; instantaneous spectrum
Abstract:

Methods such as wavelets short-term Fourier transforms and M-stationary processes have been developed to analyze the time-frequency properties of a process where the frequency changes with time. We review a new approach to this problem based on time deformation. In particular, we review G(lambda)-stationary processes and demonstrate their applicability to a wide variety of problems with time varying frequencies. These problems include bat echolocation, dolphin and whale chirp signals, as well as a variety of seismic signals. Some simulated examples are also included. Several examples are also given that show the application of these new methods to filtering signals with time varying frequencies. This latter application is referred to as Wave Match Filtering. Several new ideas are introduced, including instantaneous spectrum of a G(lambda)-stationary process.


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