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Introduction to Digital Filters
    Time Domain Digital Filter Representations
       Signal Flow Graph

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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 \end{figure}

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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