Approximate identities and the pointwise approximation of continuous wavelet transform
Jizheng Di · Journal of Zhejiang University of Technology · 2011
Like Fourier transform,there is an intimate relationship between the inverse formula of continuous wavelet transform and the approximate identities of convolution.At fact,continuous wavelet transform could be regarded as a constructing method of the approximate identities.The pointwise approximation of wavelet transform had been fully discussed previously,but was not associated with the approximate identities.This paper proves several new theorems about the pointwise approximation of continuous wavelet transform with approximate identities.Based on these theorems,the error estimates of the approximating under different conditions are given.It provides the theoretical basis for signal denoising.Finally,the numerical experiment shows that the signal noise can be removed successfully,the correctness of the theorems and usability of the relevant algorithm are verified.