Signal Flow Graph

One possible signal flow graph (or system diagram) for Eq.$ \,$(5.1) is given in Fig.5.1a for the case of $ M = 2$ and $ N = 2$. Hopefully, it is easy to see how this diagram represents the difference equation (a box labeled ``$ z^{-1}$'' denotes a one-sample delay in time). The diagram remains true if it is converted to the frequency domain by replacing all time-domain signals by their respective z transforms (or Fourier transforms); that is, we may replace $ x(n)$ by $ X(z)$ and $ y(n)$ by $ Y(z)$. $ Z$ transforms and their usage will be discussed in Chapter 6.

Figure 5.1: Signal flow graph for the filter difference equation
$ y(n) = b_0 x(n) + b_1 x(n - 1) + b_2 x(n - 2) - a_1 y(n - 1) - a_2 y(n - 2)$.
(a) Direct form I. (b) Direct form II.
\begin{figure}\input fig/kfig2p8.pstex_t

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Difference Equation