I have implemented the Fast Fourier Transform (FFT) algorithm, using the method of Cooley-Tukey. The FFT reduces the computation required in determining the Fourier Transform, which is used in several applications in science and engineering, including signal processing computations and spectral analysis. The Cooley-Tukey method primarily uses binary logic, making use of the symmetry and periodicity properties of complex exponentials. Substantial savings can be made in computation, especially when the number of input sample values is large. The FFT has been widely implemented in signal processing equipment, both in hardware and software. This implementation is in Java 1.4, running on Red Hat Linux 9. It takes as input a series of input signal samples. The output is a series of raw FFT values which are complex numbers. Admittedly, there is nothing new in this implementation. I got the oppertunity to study and understand the FFT during the course of this mini-project. This report was developed using the LATEX typesetting system on a PC running Red Hat Linux 9.