The difference equation (Eq. (5.1)) is often used as the recipe for numerical implementation in software or hardware. As such, it specifies the direct-form I (DF-I) implementation of a digital filter, one of four direct-form structures to choose from. The DF-I signal flow graph for the second-order case is shown in Fig.5.1a. The direct-form II structure, another common choice, is depicted in Fig.5.1b. The other two direct forms are obtained by transposing direct forms I and II. Chapter 9 discusses all four direct-form structures.