| Time-Frequency Analysis Based on Mono-Components Contributor(s): Dang, Pei (Author) |
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ISBN: 3659138746 ISBN-13: 9783659138744 Publisher: LAP Lambert Academic Publishing OUR PRICE: $60.53 Product Type: Paperback Published: June 2012 |
| Additional Information |
| BISAC Categories: - Mathematics |
| Physical Information: 0.36" H x 6" W x 9" (0.52 lbs) 156 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In this study, we define phase derivatives of analytic signals through non-tangential boundary limits, and consequently raise a new type of derivatives called Hardy-Sobolev derivatives for signals in the related Sobolev spaces. We prove that signals in the Sobolev spaces have well-defined phase derivatives that reduce to the classical ones when the latter exist. Based on the study of several types of phase derivatives and their properties, we mainly work on the following three subjects: (1)We extend the existing relations between the instantaneous frequency and the Fourier frequency and the related ones for smooth signals to those in the Sobolev spaces. (2) Based on the phase derivative theory and the recent result of positivity of phase derivatives of boundary limits of inner functions the theoretical foundation of all-pass filters and signals of minimum phase is established. Both the discrete and continuous signals cases are rigorously treated. (3) We study a particular type of time-frequency distribution exclusively suitable for mono-components, called transient time-frequency distribution(TTFD). For multi-components we carry on a corresponding study. |