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Consecutive minimum phase expansion of physically realizable signals with applications
Author(s) -
Mai Weixiong,
Dang Pei,
Zhang Liming,
Qian Tao
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3460
Subject(s) - hilbert transform , mathematics , computation , hilbert spectral analysis , signal (programming language) , algorithm , analytic signal , hilbert–huang transform , signal processing , convergence (economics) , mathematical analysis , fourier transform , digital signal processing , phase (matter) , energy (signal processing) , computer science , spectral density , statistics , chemistry , organic chemistry , computer hardware , economics , programming language , economic growth
In digital signal processing, it is a well know fact that a causal signal of finite energy is front loaded if and only if the corresponding analytic signal, or the physically realizable signal, is a minimum phase signal, or an outer function in the complex analysis terminology. Based on this fact, a series expansion method, called unwinding adaptive Fourier decomposition (AFD), to give rise to positive frequency representations with rapid convergence was proposed several years ago. It appears to be a promising positive frequency representation with great potential of applications. The corresponding algorithm, however, is complicated due to consecutive extractions of outer functions involving computation of Hilbert transforms. This paper is to propose a practical algorithm for unwinding AFD that does not depend on computation of Hilbert transform, but, instead, factorizes out the Blaschke product type of inner functions. The proposed method significantly improves applicability of unwinding AFD. As an application, we give the associated Dirac‐type time‐frequency distribution of physically realizable signals. Copyright © 2015 John Wiley & Sons, Ltd.