Analysis of Discrete-Time Systems in Frequency Domain

In this chapter, we apply the theory of discrete-time Fourier transformation (DTFT) presented in Chap. 6 to study the properties of discrete-time LTI systems (digital filters) in the frequency domain. The careful reader will be able to notice a lot of similarities to the frequency description of analog filters presented in Chap. 4 . Here also, the notion of the frequency response function is introduced, as well as magnitude and phase characteristics. We will present ideal and real filters of different types (low-pass, high-pass, band-pass, and band-stop) and show how to calculate the response of a system to the known input signal, including constant and harmonic excitations. A special section will be devoted to the frequency transformation method used in digital filter design.