Chapter 15 presents a detailed analysis of discrete-time signals and systems in the frequency domain, including the theory of the discrete Fourier series, the discrete-time Fourier transform, and the discrete Fourier transform, and key examples relevant for the analysis and synthesis of signals processed in the discrete transceiver blocks of a communication system. Amplitude spectra, magnitude spectra, phase spectra, and power spectra are defined and calculated for typical signals. Using a unique notation that distinguishes between energy signals and power signals, the correlation function and power or energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of linear-time-invariant systems, using the notions of impulse responses, correlation functions, and power spectral densities for both power and energy signals, is presented. The basic theory of the z-transform is also presented.