Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function

The advantages of wavelets and their promising features in various application have attracted a lot of interest and effort in recent years. In this article, the notion of two-directional biorthogonal finitely supported trivariate wavelet packets with multiscale is developed. Their properties is investigated by virtue of algebra theory, time-frequency analysis method and functional analysis method. In the final, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are established

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7. Time-Frequency Analysis and Wavelet Packets

Wavelets ◽

10.1137/1.9780898718119.ch7 ◽

2001 ◽

pp. 105-115

Keyword(s):

Frequency Analysis ◽

Wavelet Packets ◽

Time Frequency Analysis ◽

Time Frequency

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Time-frequency analysis and noise suppression with shift-invariant wavelet packets

Ultra- Wideband Short-Pulse Electromagnetics 4 (IEEE Cat. No.98EX112) ◽

10.1109/uwbsp.1998.818974 ◽

2002 ◽

Cited By ~ 1

Author(s):

I. Cohen ◽

S. Raz ◽

D. Malah

Keyword(s):

Frequency Analysis ◽

Noise Suppression ◽

Wavelet Packets ◽

Time Frequency Analysis ◽

Time Frequency

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An Algorithm and Characteristics Concerning a Sort of Orthogonal Ternary Matrix-Valued Frame Wavelet Packs

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.204-210.2225 ◽

2011 ◽

Vol 204-210 ◽

pp. 2225-2228

Author(s):

Hong Lin Guo ◽

Rong Qian Wang

Keyword(s):

Functional Analysis ◽

Frequency Analysis ◽

Multiresolution Analysis ◽

Matrix Theory ◽

Orthogonal Matrix ◽

Wavelet Packets ◽

Analysis Method ◽

Orthonormal Wavelet ◽

Time Frequency Analysis ◽

Time Frequency

In this work, the notion of matrix-valued multiresolution analysis of space L2(Rn, Cs×s) is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space L2(Rn, Cs×s) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

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The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1147 ◽

2010 ◽

Vol 439-440 ◽

pp. 1147-1152

Author(s):

Jin Cang Han ◽

Yang Li

Keyword(s):

Functional Analysis ◽

Frequency Analysis ◽

Multiresolution Analysis ◽

Orthonormal Basis ◽

Matrix Theory ◽

Orthogonal Matrix ◽

Wavelet Packets ◽

Analysis Method ◽

Time Frequency Analysis ◽

Time Frequency

The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

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The Study of Compactly Supported Orthogonal Two-Direction Vector-Valued Wavelet Packet

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.919-921.1340 ◽

2014 ◽

Vol 919-921 ◽

pp. 1340-1344

Author(s):

Lan Li

Keyword(s):

Functional Analysis ◽

Frequency Analysis ◽

Wavelet Packet ◽

Wavelet Packets ◽

Direction Vector ◽

Analysis Method ◽

Time Frequency Analysis ◽

Time Frequency ◽

Algebra Theory ◽

Vector Valued

The concept of two-direction vector-valued wavelet packets is proposed. An approach for constructing orthogonal two-direction vector-valued wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, algebra theory and functional analysis method. Orthogonality formulas concerning these two-direction vector-valued wavelet packets are established.

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