Wavelet series approximation using wavelet function with compactly support

Abstract

The Wavelets generated by Scaling Function with Compactly Support are useful in various applications especially for reconstruction of functions. Generally, the computational process will be faster if Scaling Function support descends, so computational errors are summarized from one level to another level. In this article, the convergences of wavelet series are evaluated under certain conditions by applying wavelets with Compactly Support. In fact, an approximation with such wavelets is obtained for wavelet series. This approximation is used in several applications such as compression, decomposition and reconstruction of functions.

Keywords: Scaling function; wavelet function; periodic multiresolution analysis (PMRA);
wavelet series; compactly support.