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qr code vb.net library Analog Signal in Sampled Form. Unit Impulse Notation in .NET framework
Analog Signal in Sampled Form. Unit Impulse Notation Recognizing Code 128 In Visual Studio .NET Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET framework applications. Drawing Code128 In .NET Framework Using Barcode encoder for Visual Studio .NET Control to generate, create USS Code 128 image in VS .NET applications. Let v t denote the instantaneous continuous values of an analog signal. Then one way of GRAPHICALLY representing the SAMPLED FORM of v t is shown in Fig. 331, where T is the uniform amount of time between samples. Scanning Code 128B In .NET Framework Using Barcode reader for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Printing Barcode In Visual Studio .NET Using Barcode creator for .NET Control to generate, create bar code image in Visual Studio .NET applications. CHAPTER 13 The Digital Processor
Bar Code Scanner In VS .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications. Creating ANSI/AIM Code 128 In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create Code128 image in VS .NET applications. Fig. 331
Make Code 128A In .NET Framework Using Barcode creator for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Code 128 Code Set B Creator In VB.NET Using Barcode generator for .NET Control to generate, create Code 128 Code Set A image in Visual Studio .NET applications. In the gure, each distance line, drawn from the horizontal axis, represents the value of v t at that particular sampling instant. Thus v 2T value of v t at t 2T v T value of v t at t T v 0 value of v t at t 0 v T value of v t at t T v 2T value of v t at t 2T and so on, thus, v nT value of v t at any nth sampling instant Now let s assume the analog signal starts at some time t 0, that is, v t 0 for t < 0. For this condition, all the sample values to the left of the origin in the above gure are, of course, equal to zero. Then the equation for vs t , the sampled form of v t , can be written in terms of timedelayed unit impulses;* thus vs t v 0 t v T t T v 2T t 2T v nT t nT 571 DataBar Drawer In VS .NET Using Barcode generator for .NET framework Control to generate, create DataBar image in VS .NET applications. Painting Barcode In .NET Framework Using Barcode drawer for .NET Control to generate, create barcode image in VS .NET applications. where n is a positive integer including zero, n 0; 1; 2; 3; . . . . Because of the unit impulse factors, vs t 0 at all times EXCEPT at the instants t 0; t T; t 2T, and so on, to t nT. At each such instant one of the terms in eq. (571) will not be equal to zero; for example, at t 2T, all the terms in the equation are equal to zero except the one term v 2T t 2T . The graphical representation of eq. (571) at t 2T is shown below. Print GS1  12 In .NET Framework Using Barcode maker for VS .NET Control to generate, create UPC Symbol image in Visual Studio .NET applications. GTIN  12 Creator In Visual Studio .NET Using Barcode creation for .NET Control to generate, create GTIN  12 image in .NET framework applications. Immediately following the instant at t 2T, all terms in eq. (571) become and remain equal to zero until the time t 3T, at which time only the term v 3T t 3T is not equal to zero; the situation at t 3T is shown graphically in the following gure. Bar Code Creator In ObjectiveC Using Barcode printer for iPad Control to generate, create barcode image in iPad applications. Print Code 39 Full ASCII In ObjectiveC Using Barcode creation for iPhone Control to generate, create Code 39 Extended image in iPhone applications. * See note 31, then note 32, in Appendix.
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Encoding Bar Code In .NET Using Barcode drawer for Reporting Service Control to generate, create barcode image in Reporting Service applications. Recognizing Barcode In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Let us note, now, that eq. (571) can also be written using the convenient sigma or summation notation, thus vs t Decoding UPC Symbol In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Drawing Barcode In None Using Barcode creation for Online Control to generate, create bar code image in Online applications. n 1 X n 0
v nT t nT
572 P in which the symbol is the capital Greek letter sigma. The sigma notation is read as the SUM of all such terms from n 0 to n equals in nity, where here in nity means that n, the number of terms, must be allowed to become in nitely great. The zTransform
Equation (572) is called a time series, because the independent variable is the real quantity time, t. It has been discovered, however, that the ALGEBRAIC WORK associated with the manipulation of sampled analog signals is much simpli ed if the situation in Fig. 331 is mathematically de ned in terms of a COMPLEX VARIABLE z instead of the real variable time. This is done as follows. Let us begin by arbitrarily writing down the following in nite series, in which v 0 ; v T ; v 2T and so on are the actual sampled values of an analog signal, and where z is the complex variable referred to above, F z v 0 v T z 1 v 2T z 2 v nT z n where z A j!T in which A is a positive real constant, with the restriction that A be greater than 1 A > 1 . Note that now the independent variable is sinusoidal FREQUENCY, ! 2f ; thus we are now said to be working in the frequency domain instead of the time domain. The quantity F z above is called the ztransform of the sequence of samples. As always, T is the constant time between samples. Note now that the above can be neatly summarized by making use of the sigma notation, thus F z where z A j!T and where A > 1.* * Basically the value of A, in the summation of a given v nT series, must be large enough so that, as n ! 1, A n decreases faster than the sum of the v nT series increases; this allows us to get a de nite answer for F z , instead of the indeterminate answer in nitely great.

