The discrete Fourier transform or DFT is the frequency domain workhorse of signal processing. It is the only Fourier representation that can be evaluated with a computer. In this series of 13 lessons you will learn how the DFT is related to the discrete-time Fourier transform, and how the DFT can be used to approximate the Fourier transform. You will learn the principles behind the fast Fourier transform algorithm for efficiently computing the DFT. You will also learn the principles of circular convolution and how to implement filtering using the DFT. This series is essential for everyone interested in spectral analysis of data or any computational Fourier analysis application.