AS YOU MAY RECALL, A GOAL OF THIS COURSE has been to introduce some of the tools of applied mathematics with an underlying theme of finding the connection between analog and discrete signals. We began our studies with Fourier series, which provided representations of periodic functions. We then moved on to the study of Fourier transforms, which represent functions defined over all space. Such functions can be used to describe analog signals. However, we cannot record and store analog signals. There is an uncountable amount of information in analog signals. We record a signal for a finite amount of time and even then we can only store samples of the signal over that time interval. The resulting signal is discrete. These discrete signals are represented using the Discrete Fourier Transform (DFT).