CONVERGENCE OF THE DISCRETE WAVELET TRANSFORM

摘要

The discrete wavelet transform; depending of the pair of integers (m, n), applied to functions f in L~2(R) with respect to an admissible function h in L~2(R) of class C~∞ with compact support, is used to prove that f is continuous at x = 0, and furthermore at any x = b in R if and only if there exists the convergence of the discrete wavelet transform, as (m, n) → (-∞, n_1) for any integer n_1.