非调和小波基与时频局部化函数的逼近

Nonharmonic wavelet basis and approximation function with time-frequency localization

当正交小波基ψm,n=2-m/2ψ(2-mx-n),m,n∈Z的整平移出现扰动而变为λn(λn-n<1)时,该小波基可构成L2(R)空间的Riesz基ψm,λm=2-m/2ψ(2-mx-λn).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.

Wavelets are functions generated by translating and dilating a function or a finite number of functions. In thi spaper, we consider that the orthonormal basis (ψm,n)m,n∈Z for L2(R) is replaced by the nonharmonic wavelet basis ψm,λn=2-m/2 ψ(2-m x-λn), m,n∈Z,λn-n≤1 such that f∈L2(R) has nonharmonic wavelet expression f(x)=∑m,n cm,n ψm,λn. (ψm,λn)m,n∈Z is used to approximate function f which is 'essentially localized' in timefrequency. The result in Dauberchies is developed.