非调和小波基与时频局部化函数的逼近

非调和小波基与时频局部化函数的逼近

石智1,2;宋国乡1

(1. 西安电子科技大学理学院，陕西西安 710071;
2. 西安建筑科技大学理学院，陕西西安 710055)

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2003-04-20 发布日期:2003-04-20

Nonharmonic wavelet basis and approximation function with time-frequency localization

SHI Zhi1,2;SONG Guo-xiang1

(1. School of Science, Xidian Univ., Xi’an 710071， China;
2. School of Science, Xi'an Univ. of Arch. & Tech., Xi'an 710055， China)

Received:1900-01-01 Revised:1900-01-01 Online:2003-04-20 Published:2003-04-20

摘要/Abstract

摘要： 当正交小波基ψ_m,n=2^-m/2 ψ(2^-m x-n)，m,n∈Z的整平移出现扰动而变为λ_n(|λ_n-n|＜1)时，该小波基可构成L²(R)空间的Riesz基ψ_{m,λ_m}=2^-m/2 ψ(2^-m x-λ_n). 这种小波基称为非调和小波基. 对具有时频局部化的函数f(x)，可用这种小波逼近，从而推广了Dauberchies相应的结果.

关键词: 非调和小波, 时频局部化, 基逼近

Abstract:

Wavelets are functions generated by translating and dilating a function or a finite number of functions. In this paper, we consider that the orthonormal basis (ψ_m,n )_m,n∈Z for L²(R) is replaced by the nonharmonic wavelet basis ψ_{m,λ_m}=2^-m/2 ψ(2^-m x-λ_n), m,n∈Z, (|λ_n-n|≤1 such that f∈L²(R) has nonharmonic wavelet expression f(x)=∑_m,n c_m,nψ_{m,λ_m}·(ψ_m,n )_m,n∈Z is used to approximate function f which is "essentially localized" in time-frequency. The result in Dauberchies is developed.

Key words: nonharmonic wavelet basis, time-frequency localization, essentially localized

中图分类号:

O174.2

石智1;2;宋国乡1. 非调和小波基与时频局部化函数的逼近[J]. J4, 2003, 30(2): 271-276.

SHI Zhi1;2;SONG Guo-xiang1.

Nonharmonic wavelet basis and approximation function with time-frequency localization

[J]. J4, 2003, 30(2): 271-276.

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