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: System diagram for the filter difference equation