The ascertainment of scale sampling step for numerical realization of the continuous wavelet transform

One of the key discrete approach for the numerical realization of the continuous wavelet transform is to ascertain the ripple capability of corresponding numerical wavelet filter, which is the requirement and basic for wavelet analytic engineering achievement and research in theory. This article disserts the basic theory for the ascertainment of corresponding numerical wavelet filter´s ripple capability for numerical realization of the continuous wavelet transforms. According to the highest numeric angle frequency of signal is or below π, in these two cases the article respectively deduces the corresponding numerical wavelet filter´s ripple capability of Gauss function´s each phases differential coefficient for even or odd symmetric mother wave in the numerical realization of the continuous wavelet transform when even dot-and-grid sampling is adopted. These useful conclusions solve a fundamental issue of wavelet analyses in engineering practice and research in theory.