The Fast Fourier Transform (FFT) is predominantly used in the signal processing community to perform time-frequency domain transforms. This chapter describes tradeoffs when mapping the FFT to a GPUs. It presents different implementations of the algorithm for computing the FFT. The chapter includes a design strategy for mapping the FFT computation to a GPU. It also provides example code showing how to develop OpenCL code to compute the 1D and 2D FFT, and includes the host code written in C. The chapter provides the performance results of the execution of the FFT code as run on AMD and Nvidia GPUs.