First, the real exponential is used to explain the concept of transform in reducing the multiplication operation into much simpler addition operation. Then, the complex exponential with a pure imaginary exponent is introduced and the relation between the exponential and sinusoidal signals is established. It is pointed out that the DFT gives a complex exponential polynomial representation of a signal. The orthogonality property of the complex exponentials is used to derive the definitions of the DFT and the IDFT. The least squares error criterion of signal representation is established. Several examples of computing the DFT and IDFT are presented using the matrix form of the DFT and the IDFT. An image processing application concludes the chapter.