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barcode generator for ssrs TRANSFORM ANALYSIS O F SYSTEMS in Software
TRANSFORM ANALYSIS O F SYSTEMS Code 128 Code Set B Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Print Code 128 Code Set A In None Using Barcode generator for Software Control to generate, create Code128 image in Software applications. [CHAP. 5
Read Code128 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Code 128 Code Set A Creator In Visual C#.NET Using Barcode encoder for .NET Control to generate, create Code 128C image in .NET applications. Thus,$ipping one or more zeros of the system function about the unit circle does not change the magnitude of the frequency response. Generating Code 128 Code Set A In VS .NET Using Barcode generator for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Making Code128 In .NET Framework Using Barcode generation for .NET framework Control to generate, create Code 128A image in VS .NET applications. EXAMPLE 5.4.1 For a filter that has a system function
Code128 Creator In Visual Basic .NET Using Barcode encoder for .NET Control to generate, create Code 128 Code Set C image in .NET applications. ECC200 Generator In None Using Barcode encoder for Software Control to generate, create ECC200 image in Software applications. the magnitude of the frequency response will not be changed if it is cascaded with the allpass filter Printing Bar Code In None Using Barcode creator for Software Control to generate, create barcode image in Software applications. Print USS Code 128 In None Using Barcode creation for Software Control to generate, create Code 128A image in Software applications. This allpass filter flips the zero at z = 0.2 in H(z) to its reciprocal location, z = 5, and the new filter has a system function Encode Barcode In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. Drawing EAN / UCC  13 In None Using Barcode creation for Software Control to generate, create GS1  13 image in Software applications. 5.5 MINIMUM PHASE SYSTEMS
Draw Delivery Point Barcode (DPBC) In None Using Barcode encoder for Software Control to generate, create Delivery Point Barcode (DPBC) image in Software applications. Draw Code 128A In None Using Barcode generation for Microsoft Word Control to generate, create Code 128B image in Word applications. A stable and causal linear shiftinvariant system with a rational system function of the form given in Eq. (5.2) has all of its poles inside the unit circle, lakI < 1. The zeros, however, may lie anywhere in the zplane. In some applications, it is necessary to constrain a system so that its inverse, G(z) = l/H(z), is also stable and causal. I This requires that the zeros of H (z) lie inside the unit circle, JBk < I. A stable and causal filter that has a stable and causal inverse is said to have minimum phase. Equivalently, we have the following definition: Barcode Recognizer In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Printing UCC.EAN  128 In C# Using Barcode encoder for .NET Control to generate, create EAN / UCC  13 image in .NET framework applications. Definition: A rational system function with all of its poles and zeros inside the unit circle is said to be have minimum phase. Generate Data Matrix In Java Using Barcode creator for Java Control to generate, create Data Matrix 2d barcode image in Java applications. UPCA Supplement 2 Maker In .NET Framework Using Barcode creation for ASP.NET Control to generate, create UPCA image in ASP.NET applications. A minimum phase system is uniquely defined by the magnitude of its Fourier transform, IH(eJm)(.The procedure to find H (z) from 1 H (ejm)\is as follows. Given \ H (ejW)l,we find 1 H (ej")12, which is a function of cos(ko). Then, by replacing cos(kw) with C(zk zpk), we have Code 39 Extended Decoder In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Print Matrix 2D Barcode In VB.NET Using Barcode maker for VS .NET Control to generate, create Matrix Barcode image in Visual Studio .NET applications. Finally, the minimum phase system is then formed from the poles and zeros of G ( z )that are inside the unit circle. EXAMPLE 5.5.1
Let H(z) be a minimum phase system with a Fourier transform magnitude
I ~(e'")l*= $  f cosw
Expressing cos w in terms of complex exponentials, and replacing
with z and e1" with z', we have
Thus, the minimum phase system is
CHAP. 51
TRANSFORM ANALYSIS OF SYSTEMS
A stable and causal system may always be factored into a product of a minimum phase system with an allpass system: (5.17) H ( z ) = Hmin(z).Hap(z) The procedure for performing this factorization is as follows. First, all of the zeros of H ( z ) that are outside the unit circle are reflected inside the unit circle to their conjugate reciprocal location. The resulting system function is minimum phase, Hmin(z). Then, the allpass filter is selected so that it reflects the appropriate set of zeros of Hmin(z) back outside the unit circle. EXAMPLE 5.5.2 For the system function the minimum phase factor is
Then, to reflect the zero at z = 0.5 back outside the unit circle to z = 2, we use the allpass factor Two properties of minimum phase systems are as follows. First, of all systems that have the same Fourier transform magnitude, the minimum phase system has the minimum group delay. This follows from the factorbe ization given in Eq. (5.17). Specifically, let Hmin(z) a minimum phase system, and let H (z) be another system with the same magnitude. The group delay for H ( z ) may be written as where rap(u) the group delay of a stable and causal allpass system. Because tap(u) 0, the group delay of H ( z ) is > will be larger than the group delay of the minimum phase system Hmi,,(z). Furthermore, because the phase is the negative of the integral of the group delay, the minimum phase system is also said to have the minimum phaselag. The second property of minimum phase systems is that they have the minimum energy delay. Specifically, if hmin(n) the unit sample response of a minimum phase system, and h ( n ) is the unit sample response of another is causal system that has the same magnitude response, for any n 3 0.
FEEDBACK SYSTEMS
Feedback systems are used in many applications such as stabilization of unstable systems, compensation of nonideal elements, tracking systems, and inverse system design. The general configuration of a discretetime feedback system is shown in Fig. 56. The system N ( z ) is referred to as the system function of the forward path, and G ( z )is referred to as the system function of thefeedbuck path. The system function relating the input x ( n ) to the output y(n) is called the closedloop system function and is denoted by Q(z). Because

