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ssrs 2d barcode the input x ( n ) and output y(n) are related by the linear constant coefficient difference equation in Software
the input x ( n ) and output y(n) are related by the linear constant coefficient difference equation Read ANSI/AIM Code 128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Creating Code 128 In None Using Barcode generator for Software Control to generate, create Code128 image in Software applications. This difference equation defines a sequence of operations that are to be performed in order to implement this system. However, note that this system may also be implemented with the following pair of coupled difference equations: Code128 Scanner In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Making ANSI/AIM Code 128 In C# Using Barcode generation for .NET Control to generate, create Code128 image in Visual Studio .NET applications. With this implementation, it is only necessary to provide one memory location to store w(n  I), whereas Eq. (8.1)requires two memory locations, one to store y(n  I) and one to store x(n  1). This simple example illustrates that there is more than one way to implement a system and that the amount of computation and/or memory required will depend on the implementation. In addition, the implementation may affect the sensitivity of the filter to coefficient quantization. and the amount of roundoff noise that appears at the output of the filter. In this chapter, we look at a number of different ways to implement a linear shiftinvariant discretetime system and look at the effect of finite word lengths on these implementations. Draw Code128 In Visual Studio .NET Using Barcode printer for ASP.NET Control to generate, create Code 128B image in ASP.NET applications. Make ANSI/AIM Code 128 In VS .NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128 image in .NET applications. 8.2 DIGITAL NETWORKS
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(b) Multiplier.
Fig. 81. Notation used for an adder, multiplier, and delay in a digital network.
Fig. 82. Signal flowgraph consisting of nodes, branches, and node variables. Node j represents an adder, and node k is a branch point. EXAMPLE 8.2.1 Consider the firstorder discretetime system described by the difference equation Shown in the figure below is a block diagram for this system.
Using a signal flowgraph, this system is represented as follows: CHAP. 81
IMPLEMENTATION OF DISCRETETIME SYSTEMS
8.3 STRUCTURES FOR FIR SYSTEMS
A causal FIR filter has a system function that is a polynomial in zp': H (z) = h(n)zpn
For an input x(n), the output is
For each value of n, evaluating this sum requires (N I) multiplications and N additions. The following subsections describe several different realizations of this system. 8.3.1 Direct Form
The most common way to implement an FIR filter is in direct form using a tapped delay line as shown in the figure below. h(N  I ) y(n) This structure requires N I multiplications, N additions, and N delays. However, if there are some symmetries in the unit sample response, it may be possible to reduce the number of multiplications (see the section on linear phase filters). 8.3.2 Cascade Form
For a causal FIR filter, the system function may be factored into a product of firstorder factors, where a for k = 1 , . . . , N are the zeros of H (z). If h(n) is real, the complex roots of H(z) occur in complex k conjugate pairs, and these conjugate pairs may be combined to form secondorder factors with real coefficients, Written in this form, H (z) may be implemented as a cascade of secondorder FIR filters as illustrated in Fig. 83.

