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,λm=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,λm·(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