Time-Frequency Analysis Based on Mono-Components: Some functional analysis foundations of signal processing - Softcover

Dang, Pei

Softcover

ISBN 10: 3659138746 ISBN 13: 9783659138744

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

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.

About this title

About the Author

Academic Qualifications:Doctor (2007-2011) University of Macau; Master (2005-2007) Wuhan University;Bachelor (2001-2005) Henan Normal University.Research Interests: Signal processing, Time-Frequency analysis, Harmonic analysis in Euclidean spaces.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• ISBN 10: 3659138746
• ISBN 13: 9783659138744
• Binding: Paperback
• Language: English
• Number of pages: 156