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Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method

Tavallali, Peyman and Hou, Thomas Y. and Shi, Zuoqiang (2014) Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. Multiscale Modeling and Simulation, 12 (4). pp. 1458-1493. ISSN 1540-3459. doi:10.1137/140957767.

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Analysis and extraction of strongly frequency modulated signals have been a challenging problem for adaptive data analysis methods, e.g., empirical mode decomposition [N.E. Huang et al., R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), pp. 903--995]. In fact, many of the Newtonian dynamical systems, including conservative mechanical systems, are sources of signals with low to strong levels of frequency modulation. Analysis of such signals is an important issue in system identification problems. In this paper, we present a novel method to accurately extract intrawave signals. This method is a descendant of sparse time-frequency representation methods [T.Y. Hou and Z. Shi, Appl. Comput. Harmon. Anal., 35 (2013), pp. 284--308, T.Y. Hou and Z. Shi, Adv. Adapt. Data Anal., 3 (2011), pp. 1--28]. We will present numerical examples to show the performance of this new algorithm. Theoretical analysis of convergence of the algorithm is also presented as a support for the method. We will show that the algorithm is stable to noise perturbation as well.

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Additional Information:© 2014 Society for Industrial and Applied Mathematics. Received by the editors February 19, 2014; accepted for publication (in revised form) July 10, 2014; published electronically October 23, 2014. This research was supported in part by AFOSR MURI grant FA9550-09-1-0613, DOE grant DE-FG02-06ER25727, and NSF grants DMS-1159138 and DMS-1318377. This author’s research was supported in part by NSFC grant 11201257.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0613
Department of Energy (DOE)DE-FG02-06ER25727
National Natural Science Foundation of China (NSFC)11201257
Subject Keywords:sparse time-frequency representation, instantaneous frequency, intrawave frequency modulation
Issue or Number:4
Classification Code:AMS subject classifications: 94A12, 65T99
Record Number:CaltechAUTHORS:20150202-093859868
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Official Citation:Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method Peyman Tavallali, Thomas Y. Hou, and Zuoqiang Shi Multiscale Modeling & Simulation 2014 12:4, 1458-1493
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54284
Deposited By: Ruth Sustaita
Deposited On:02 Feb 2015 19:18
Last Modified:10 Nov 2021 20:31

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