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qr code vb.net source Note 31. in .NET
Note 31. Decode Code128 In VS .NET Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET applications. Painting Code 128 In .NET Framework Using Barcode generation for VS .NET Control to generate, create Code 128A image in .NET applications. Shifting Theorem
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Here we wish to introduce the very useful concept of unit impulse. Let us begin with drawings A, B, and C in Fig. 38A. As illustrated, the particular form of pulse we ll be interested in here will always have a time duration of a seconds and a value equal to 1=a; thus, since, a 1=a 1, such a pulse will always enclose unit area, as shown in the gure. Appendix
Fig. 38A
Now, in C, let us allow a to approach zero as a limiting value a ! 0 which, in turn, will make the value of the pulse, 1=a, become in nitely great 1=a ! 1), with the area enclosed by the pulse always remaining equal to 1. In words, we are hypothesizing, at t 0, the existence of a pulse of in nitely great amplitude but vanishingly short time duration, the pulse always enclosing unit area. The hypothetical pulse so described is called a UNIT IMPULSE, and is denoted by the symbol t , which can be read as delta of t ( d is the small Greek letter delta ). Such a pulse cannot, of course, exist in the real physical world. It is, nevertheless, a very useful mathematical device, for the following reasons. First of all, very short, highvalued pulses of voltage and current do exist in the real world, and such actual pulses, when applied to a network, have the same general e ect as would the application of a theoretical impulse to the network. In other words, the theoretical analysis of a network to applied t yields results that will closely approximate the actual results produced by the application of a very high, sharp, pulse to the network. A second reason lies in the fact that a function of time t can be expressed in terms of a particular secondary variable s, where s is a complex number of the form s a j!. This is important, because the work required in circuit analysis can often be greatly reduced when carried out in terms of s instead of t. This is especially true if we re investigating the e ect of applying an impulse type of signal to a network. This is because it turns out that t is simply replaced by 1 when working in terms of s, a fact that can considerably reduce the algebraic complications in impulsetype problems. Lastly, t is a convenient symbol to use in writing sampling equations, which let us discuss in more detail, as follows. First, it will be convenient to refer to t as an impulse of unit strength. Then the notation A t will naturally be called an impulse of strength A. Hence, by note 31, the notation A t nT will denote an impulse of strength A shifted nT units to the right. GRAPHICALLY, an impulse is represented by a vertical line with arrowhead, with notation given alongside the line. Thus, graphically, the three impulse cases just mentioned above would appear as illustrated in the following.

