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Sparse Time-Frequency Data Analysis: A Multi-Scale Approach


Tavallali, Peyman (2014) Sparse Time-Frequency Data Analysis: A Multi-Scale Approach. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9TT4NXD.


In this work, we further extend the recently developed adaptive data analysis method, the Sparse Time-Frequency Representation (STFR) method. This method is based on the assumption that many physical signals inherently contain AM-FM representations. We propose a sparse optimization method to extract the AM-FM representations of such signals. We prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic STFR, which extends the method to tackle problems that former STFR methods could not handle, including stability to noise and non-periodic data analysis. This is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. Moreover, we propose a new STFR algorithm to study intrawave signals with strong frequency modulation and analyze the convergence of this new algorithm for periodic signals. Such signals have previously remained a bottleneck for all signal processing methods. Furthermore, we propose a modified version of STFR that facilitates the extraction of intrawaves that have overlaping frequency content. We show that the STFR methods can be applied to the realm of dynamical systems and cardiovascular signals. In particular, we present a simplified and modified version of the STFR algorithm that is potentially useful for the diagnosis of some cardiovascular diseases. We further explain some preliminary work on the nature of Intrinsic Mode Functions (IMFs) and how they can have different representations in different phase coordinates. This analysis shows that the uncertainty principle is fundamental to all oscillating signals.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Data analysis, adaptive, signal processing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:W.P. Carey & Co., Inc., Prize in Applied Mathematics, 2014
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hou, Thomas Y.
Thesis Committee:
  • Hou, Thomas Y. (chair)
  • Owhadi, Houman
  • Gharib, Morteza
  • Beck, James L.
Defense Date:9 May 2014
Record Number:CaltechTHESIS:05152014-141711934
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8236
Deposited By: Peyman Tavallali
Deposited On:29 Sep 2016 21:53
Last Modified:04 Oct 2019 00:04

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