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Generalizations and Applications of the Linear Chirp.: (English)

Generalizations and Applications of the Linear Chirp.: (English)

          
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About the Book

In the analysis of time series data for which the frequency changes with time, commonly used methods have been wavelets (Percival and Walden, 2000), short-term Fourier transforms (Gabor, 1946 and Wigner, 1932), and time deformation (Gray and Zhang 1988, Gray, Vijverberg, and Woodward, 2005, Jiang, Gray, and Woodward, 2006, and Choi, Woodward, and Gray, 2006). The time deformation approach applies an appropriate transformation to the time axis to produce a process which is stationary so that standard approaches for analyzing stationary data can be used. Processes which are transformed to a stationary process after transformation of the time scale are called G-stationary processes. A special case of a G-stationary process is the linear chirp (L-C) stationary process (Liu, 2004), which is useful as a model for a variety of physical systems. In general, linear chirps have a frequency structure that changes linearly with time. In this thesis we generalize the L-C process studied by Liu (2004) to develop a tool which has a wide range of applications. The L-C stationary processes can be further classified into "generalized linear chirp (GLC) processes" and "GLC( p, q) chirp processes." We show that the relationship between generalized linear chirp processes and GLC(p, q) chirp processes is analogous to that between standard harmonic and ARMA models. The new methods are then applied to both simulated and actual data sets, using S+ code for analysis.


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Product Details
  • ISBN-13: 9781243481535
  • Publisher: Proquest, Umi Dissertation Publishing
  • Publisher Imprint: Proquest, Umi Dissertation Publishing
  • Height: 254 mm
  • No of Pages: 148
  • Series Title: English
  • Weight: 308 gr
  • ISBN-10: 1243481536
  • Publisher Date: 02 Sep 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 10 mm
  • Width: 203 mm

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