Time-frequency aspects of nonlinear fourier atoms
Chen Q.1; Li L.1; Qian T.2
PublisherBirkhäuser Basel
Publication PlaceBasel

In the standard Fourier analysis one uses the linear Fourier atoms {e: n ∈ ℤ}. With only the linear phases nt Fourier analysis can not expose the essence of time-varying frequencies of nonlinear and non-stationary signals. In this note we study time-frequency properties of a new family of atoms e: n ∈ ℤ, non-linear Fourier atoms, where a is any but fixed complex number with |a| < 1, and dθ(t) a harmonic measure on the unit circle parameterized by t. The nonlinear Fourier atoms {e: n ∈ ℤ} were first noted in [12] with some examples and theoretically studied in [8]. In this note we show that the real parts cos θ(t), |a| < 1, form a family of intrinsic mode functions introduced in the HHT theory [5]. We prove that for a fixed a the set {e: n ∈ ℤ}, constitutes a Riesz basis in the space L([0, 2π]). Some miscellaneous results including Shannon type sampling theorems are obtained.

KeywordHilbert-huang Transform Nonlinear Fourier Atom Sampling Theorem Time-frequency Analysis
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Document TypeBook
CollectionUniversity of Macau
Affiliation1.Faculty of Mathematics and Computer Science,Hubei University,Wuhan,P. R. China
2.Department of Mathematics Faculty of Science and Technology,University of Macau,Macao (via Hong Kong)
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GB/T 7714
Chen Q.,Li L.,Qian T.. Time-frequency aspects of nonlinear fourier atoms[M]. Basel:Birkhäuser Basel,2007.
APA Chen Q.,Li L.,&Qian T..(2007).Time-frequency aspects of nonlinear fourier atoms.Applied and Numerical Harmonic Analysis(9783764377779),287-297.
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