The Discrete Fourier Transform (DFT): Definition

This lecture covers the definition of the Discrete Fourier Transform (DFT) as a practical tool for digital signal processing, focusing on discretization of frequency, properties of the DFT, and quality of the discrete approximation. It explains how the DFT is used for periodic signals, finite duration signals, and signals of unlimited duration, highlighting the importance of the Fast Fourier Transform (FFT) algorithm. The lecture also discusses the periodic nature of the Fourier Transform of a sampled signal and the implications of signal duration on the DFT.