Nonharmonic wavelet basis and approximation function with time-frequency localization
Zhi Shi · Journal of Xidian University · 2003
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 (ψm,n)m,n∈Z for L2(R) is replaced by the nonharmonic wavelet basis ψm,λn=2-m/2 ψ(2-m x-λn), m,n∈Z,λn-n≤1 such that f∈L2(R) has nonharmonic wavelet expression f(x)=∑m,n cm,n ψm,λn. (ψm,λn)m,n∈Z is used to approximate function f which is essentially localized in timefrequency. The result in Dauberchies is developed.