Wavelets are a recent development in signal processing. These kind of functions are both well-localized in time and in frequency, and so using these to transform the signal gives insight where certain frequencies are needed. The classical way of constructing wavelets, as described by Daubechies and Meyer [3,9] is only well-suited for the real numbers, so new methods are developed for a broader range of spaces. In this paper, we describe the algorithm developed by Coifman and Maggioni [1], and the algorithm developed by Coulhon et al. [11]. Lastly, we modify the last algorithm using the finite speed of propagation property, and so we obtain a new way of developing wavelets.