Recently, the Fast Fourier Transforms (FFT) and the Discrete Wavelet Transforms (DWT) are two time series filtering methods that are used to represent the fluctuations of stocks market. In general the basic wavelet function, Haar wavelet transform is a mathematical function that cut off the data into different frequency components, satisfies some of mathematical requirements and it has better advantages than the traditional Fourier series in analyzing financial data. Fourier transform appears to have some problem associate with its transformation because it measures the data as a function of position (in frequency domain) without consider the time while wavelet transform displays their correlation as a function of scale and time (localized in both). In this study we use financial time series data taking from the Amman Stocks Market (lordan) for a certain period of time in order to understand the similarities and dissimilarities between both of them. We look for point of abrupt changes, closing price and normalized data. In addition, some numerical results will be presented using Matlab programming. © Medwell Journals, 2010.