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qr code vb.net library The Form of, and Basic Equations for, a DT Processor in .NET
The Form of, and Basic Equations for, a DT Processor Code 128 Code Set B Decoder In .NET Framework Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET applications. Encoding USS Code 128 In Visual Studio .NET Using Barcode printer for Visual Studio .NET Control to generate, create Code128 image in .NET applications. Electronic circuitry, both CT and DT, often makes use of FEEDBACK, which involves a condition in which a portion of the system OUTPUT signal is fed back into the INPUT of the system. Such feedback, when properly used, can in some cases produce very bene cial results. In regard to DT processors, those that do use feedback are said to be recursive, while those that do not are nonrecursive. Consider, now, examples of both types, beginning with Fig. 343. Code 128 Decoder In VS .NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET framework applications. Printing Bar Code In .NET Framework Using Barcode printer for .NET framework Control to generate, create barcode image in .NET framework applications. Fig. 343
Bar Code Decoder In .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. ANSI/AIM Code 128 Generator In C#.NET Using Barcode encoder for .NET Control to generate, create USS Code 128 image in Visual Studio .NET applications. In the gure note, rst of all, that the output signal y nT is not in any way fedback into the system; thus Fig. 343 is an example of a nonrecursive system. Note also that the output sequence y nT is the sum of the present or now value 2x nT and two PAST values, 3x nT T and 7x nT 2T , which occurred T and 2T sample times ago relative to the now time of nT seconds. (In the timedelay boxes the exponent 1 means unit time delay, that is, a time delay of T seconds.) Code 128A Creation In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Code 128 Creation In VB.NET Using Barcode encoder for .NET framework Control to generate, create Code 128 Code Set C image in .NET framework applications. CHAPTER 13 The Digital Processor
UPC A Printer In .NET Framework Using Barcode generation for Visual Studio .NET Control to generate, create UPCA image in VS .NET applications. Generate Barcode In .NET Using Barcode encoder for VS .NET Control to generate, create bar code image in .NET applications. In regard to interpreting a gure such as Fig. 343, we should note that, while a notation such as x nT really denotes an entire SEQUENCE of values, n 0; 1; 2; 3; . . . , we can, for convenience, think of v nT as denoting some particular sample value existing at a time nT. One more point to note is that Fig. 343 is classi ed as a secondorder processor, because it uses two delays. Next, as a second example, consider Fig. 344. Note that the output sequence y nT is fed back to the input adder after being delayed 1 sample period. Thus Fig. 344 is a simple form of recursive DT processor (of rst order, because only one delay is used). Make Bar Code In .NET Using Barcode creation for Visual Studio .NET Control to generate, create barcode image in .NET applications. Identcode Generation In Visual Studio .NET Using Barcode printer for .NET framework Control to generate, create Identcode image in VS .NET applications. Fig. 344
Making UPCA In ObjectiveC Using Barcode generation for iPhone Control to generate, create UPC Code image in iPhone applications. Painting Code128 In VB.NET Using Barcode encoder for .NET framework Control to generate, create Code128 image in VS .NET applications. Figures 343 and 344 are simple examples of DT processors and we need not, at this point in our study, worry about how they are put to work. It is important, however, that you understand the meaning of the notation. In general, processors will consist of a combination of nonrecursive and recursive types; for example, the combination of Figs. 343 and 344 to make a single processor gives Fig. 345, in which y nT y 0 nT 10y nT T Painting Bar Code In Java Using Barcode printer for Java Control to generate, create bar code image in Java applications. Recognize UPCA Supplement 5 In C# Using Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications. Fig. 345
Create Bar Code In None Using Barcode printer for Word Control to generate, create bar code image in Word applications. Reading Barcode In Visual Basic .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications. and thus y nT 2x nT 3x nT T 7x nT 2T 10y nT T With the foregoing in mind, let s agree now to adopt the notation illustrated in Fig. 346 for the general form of a DT processor. (There is a nonrecursive part to the LEFT of point R and a recursive part to the RIGHT of point R, where R is just a reference point.) Note, rst, that the value of the output at the point R (the output of the rst adder) is R nT UPC  13 Maker In Java Using Barcode drawer for Java Control to generate, create UPC  13 image in Java applications. UPC  13 Generation In Java Using Barcode generation for Java Control to generate, create EAN / UCC  13 image in Java applications. k p X k 0
bk x nT kT
CHAPTER 13 The Digital Processor
Fig. 346
Thus we have that the nal output value of the processor is y nT
k p X k 0
bk x nT kT
k q X k 1
ak y nT kT
587 or, written out in expanded form, eq. (587) becomes y nT b0 x nT b1 x nT T b2 x nT 2T bp x nT pT a1 y nT T a2 y nT 2T aq y nT qT 588 Equations (587) and (588) are called di erence equations because of the presence of the past history forms having the di erence notation nT kT . Let us now operate on eqs. (587) and (588) in such a way as to express things in terms of the ztransform. This can be done as follows. First note that, in the above equations, y nT and x nT denote sampled values of y t and x t for any particular value of n we might be interested in. However, to bring the ztransform into the picture we must summate the values of y nT and x nT over the entire range of n that there is, for n 0 to n ! 1 (in accordance with the basic de nition of eq. (573) in section 13.3). Therefore (so that we can apply eq. (573)) let us multiply both sides of eq. (588) by z n and then summate from n 0 to n ! 1; doing this, eq. (588) becomes X X X X x nT z n b1 x nT T z n bp x nT pT z n y nT z n b0 X X X a1 y nT T z n a2 y nT 2T z n aq y nT qT z n where all summations are understood to be from n 0 to n 1. Now note that (with same summation from n 0 to n 1) by eq. (573) X y nT z n Y z and by item (4), Table 2 X y nT kT z n Y z z k

