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ssrs 2d barcode CHAP. 81 in Software
CHAP. 81 Code 128 Code Set C Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Printer In None Using Barcode creation for Software Control to generate, create Code 128C image in Software applications. IMPLEMENTATION O F DISCRETETIME SYSTEMS
Scanning Code 128C In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Drawing Code 128 Code Set B In C#.NET Using Barcode generator for .NET framework Control to generate, create Code 128 Code Set B image in Visual Studio .NET applications. A simple way to write this recursion is in terms of vectors as follows: Printing Code 128 In .NET Framework Using Barcode printer for ASP.NET Control to generate, create Code 128 Code Set C image in ASP.NET applications. Code 128C Creation In Visual Studio .NET Using Barcode generation for .NET framework Control to generate, create Code 128 Code Set B image in .NET applications. EXAMPLE 8.5.1 For a secondorder FIR lattice tiller with reflection coefficient< r I = t and relating x(n) to f l(n) is I 2A'(:) = An(:) + r l ; ' ~ , , () := 1 + i  Code 128B Generator In Visual Basic .NET Using Barcode maker for Visual Studio .NET Control to generate, create USS Code 128 image in Visual Studio .NET applications. Bar Code Generation In None Using Barcode creator for Software Control to generate, create barcode image in Software applications. r2= i, the system function
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Creating Code 3 Of 9 In None Using Barcode encoder for Software Control to generate, create USS Code 39 image in Software applications. Barcode Drawer In None Using Barcode printer for Software Control to generate, create barcode image in Software applications. The recurrence formula in Eq. (8.5) provides an algorithm to find the system function A , ( z ) from the reflection coefficients r k ,k = 1,2. . . . . p. To find the reflection coefficients r r for a given system function A ,(z), we use the s t e p d o w n recu~siotz, which is given by Making ITF14 In None Using Barcode maker for Software Control to generate, create ITF14 image in Software applications. Recognize Bar Code In VS .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. In terms of the coefficients a k ( i ) ,this recursion is
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Draw ECC200 In Java Using Barcode maker for Java Control to generate, create Data Matrix 2d barcode image in Java applications. Code 128C Drawer In Java Using Barcode maker for Android Control to generate, create Code128 image in Android applications. corresponding to the secondorder FIR filter A z ( z ) = Tz = n 2 ( 2 )= Next, we find A 1 ( z ) us~ng stepdown recursion. the
Because cl,(l) = 0. r l = 0. Therefore, the reflection coefficients are
= 0 and
= l2 ' So far, we have only considered the system function relating the input .u(n) to the output f,,(n). A similar set of equations relate the input x ( n ) to the output R , , ( I I ) With the relationship between the system function A p ( z )and A',,(z)is as follows: IMPLEMENTATION OF DISCRETETIME SYSTEMS
[CHAP. 8
Thus, f,(n) and g p ( n )are related by an allpass filter, F,(z) = Hu,f(z)G,(z), where
An important property of the lattice filter is that the roots of A,(z) will lie inside the unit circle if and only if the reflection coefficients are bounded by I in magnitude: This property is the basis for the SchurCohn stability test for digital filters. Specifically, a causal filter with a system function will be stable if and only if the reflection coefficients associated with A(z) are bounded by 1 in magnitude. 8.5.2 AllPole Lattice Filters
The structure for an allpole lattice filter is shown in Fig. 814. As with the FIR lattice, a pthorder allpole filter is a cascade of p stages, with each stage being a twoport network that is parameterized by its reflection coefficient rk.The two inputs, f k ( n ) and gk1 ( n ) ,are related to the two outputs f L F ( n )and g k ( n )by a pair of I coupled difference equations: fkl(n) = fh(n)  r k ~ k  l ( n 1) gk(n) = ~ k  l ( n 1 )  + rkfk(n) The system function relating the input x ( n ) to the output y ( n ) is
where A,(z) is the polynomial that is generated by the recursion given in Eq. (8.5). In addition, note that the given in Eq. (8.7). system function relating x ( n ) to w ( n ) is an allpass filter with a system function Hap(z) Fig. 814. A pthorder allpole lattice filter. (a)The twoport network for the kth stage of the allpole lattice filter. (b) Cascade of p lattice stages. CHAP. 81
IMPLEMENTATION OF DISCRETETIME SYSTEMS
8.5.3 IZR Lattice Filters
If H ( z ) is an IIR filter with p poles and q zeros, with q 5 p, a lattice filter implementation of H ( z ) consists of two components. The first is an allpole lattice with reflection coefficients r l ,rz,. . , F, that implements I / A p ( z ) . The second is a tapped delay line with . coefficients cq(k). The structure is illustrated in Fig. 815 for the case in which p = 4. The relationship between the lattice filter coefficients cq(k)and the direct form coefficients bq(k) is given by Similarly, a recursion that generates the coefficients cq(k)from the coefficients h q ( k )is
This recursion is initialized with c q ( q )= bq(9). EXAMPLE 8.5.3
A thirdorder lowpass elliptic filter with a cutoff frequency of w,. = 0 . 5 ~ a system function has To implement this filter using a lattice filter structure, we first transform the denominator coefficients into reflection coefficients. Using the stepdown recursion, we find

