Discrete Fourier Transform
Discrete Fourier transform (DFT) is a frequency domain representation of finite-length discrete-time signals. It is also used to represent FIR discrete-time systems in the frequency domain. As the name implies, DFT is a discrete set of frequency samples uniformly distributed around the unit circle in the complex frequency plane that characterizes a discrete-time sequence of finite duration. DFT is also intrinsically related to the DTFT, as we will see in this chapter. Because DFT is a finite set of frequency samples, it is a computational tool to perform filtering and related operations. There is an efficient algorithm known as the fast Fourier transform (FFT) to perform filtering of long sequences, power spectrum estimation, and related tasks. We will learn about the FFT in this chapter as well.