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

Language: English

Published by LAP LAMBERT Academic Publishing, 2012

3659138746 / 9783659138744

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.…

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Title
Time-Frequency Analysis Based on Mono-Components : Some functional analysis foundations of signal processing
Author
Pei Dang
Publisher
LAP LAMBERT Academic Publishing
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3659138746
ISBN 13
9783659138744
Item weight
250 grams
Dimensions
220x150x10 mm

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