Shannon function is a function with good filter but bad local character, Gauss window function with the character of controlling wavelet attenuation and local but bad low-pass. Shannon and Gauss function are used to construct a new type of wavelet function in this paper, there are father wavelet meeting the need of low-pass, firstorder and second-order mother wavelets meeting the need of band-pass, what is more, we discuss their character of orthogonality, completeness and compactly supported, taking GPS data for example, we analyze its smoothing and compress effect, marginal effect and detect singular point to get some useful conclusions, it will be a significant method for GPS data processing.