This is the first video in an 18-video series on Fourier Analysis of Discrete-Time Signals. In this first video we describe one of our primary goals, namely, writing a discrete-time signal as a weighted combination of complex exponentials. Trying to write a discrete-time signal in this form will eventually leads to the derivation of the Discrete-Time Fourier Series (DTFS) and Discrete-Time Fourier Transform (DTFT).
The DTFS is used to represent periodic discrete-time signals in the frequency domain. It's continuous-time counterpart studied previously is the Fourier Series (FS).
The DTFT is used to represent non-periodic discrete-time signals in the frequency domain. It's continuous-time counterpart studied previously is the Fourier Transform (FT).