Wavelet and Fourier transform are the common methods used in signal and image compression. Wavelet transform (WT) are very powerful compared to Fourier transform (FT) because its ability to describe any type of signals both in time and frequency domain simultaneously while for FT, it describes a signal from time domain to frequency domain. Because of that, the performance of FT is outperformed by the impressive ability of WT for most type of signals (stationary or non-stationary). In this paper, we will discuss the use of Fast Fourier Transform (FFT) and Discrete Wavelet Transform (DWT) for signal compression. We do the numerical experiment by considering three types of signals and by applying FFT and DWT to decompose those signals. For DWT, various wavelet filters such as Haar (2 filters) and Daubechies (up to 10 filters) are used. All the numerical results were done by using Matlab programming. © 2011 IEEE.