Continuous wavelet transforms

In this paper, we propose a new type of Continuous wavelet transform. However we discretize variables of integral a and b, any numerical integral has a high resolution, and a does not appear in the denominator of the integrand. Furthermore, we give two discrezitation methods of the new wavelet transform. For the one-dimensional situation, we give quadrature formula of the discretized inverse wavelet transform. For the multi-dimensional situation, we develop the commonly wavelet network based on the discretized inverse wavelet transform of the new wavelet transform. Finally, die numerical examples show that the continuous wavelet transform constructed in this paper has higher computing accuracy, compared with the classical continuous wavelet transform.