 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
qr code vb.net library Stability and Instability. Poles and Zeros in VS .NET
Stability and Instability. Poles and Zeros Scanning Code128 In VS .NET Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications. Encoding Code 128B In Visual Studio .NET Using Barcode generator for .NET Control to generate, create ANSI/AIM Code 128 image in .NET applications. It is possible for a recursive DT processor to become unstable under certain conditions. The desired condition of stability and the undesired condition of instability can be de ned in general terms as follows. Let a momentary signal, such as the unit pulse of Fig. 332, be applied to the input of a recursive DT processor. If the OUTPUT of the processor dies out and becomes zero as time increases, the processor is STABLE; if, however, the output does not become zero as time increases, the processor is UNSTABLE. Let us take, as an example to illustrate the basic possibilities, the simple recursive processor shown in Fig. 348. Code 128 Scanner In .NET Framework Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Make Bar Code In VS .NET Using Barcode maker for VS .NET Control to generate, create barcode image in .NET applications. Fig. 348
Reading Bar Code In .NET Framework Using Barcode reader for .NET framework Control to read, scan read, scan image in VS .NET applications. Code 128 Code Set C Generation In C#.NET Using Barcode generation for .NET Control to generate, create USS Code 128 image in VS .NET applications. For brevity here we ll denote the unit pulse by 1, as shown in the gure. Note that the above is the same as Fig. 344, except that now the input is given to be the unit pulse, x nT p nT 1, and the multiplier constant is denoted by a. It is the VALUE OF ANSI/AIM Code 128 Drawer In .NET Using Barcode encoder for ASP.NET Control to generate, create Code 128C image in ASP.NET applications. Encoding Code 128B In Visual Basic .NET Using Barcode creator for .NET framework Control to generate, create USS Code 128 image in .NET applications. CHAPTER 13 The Digital Processor
Generate Barcode In VS .NET Using Barcode generation for Visual Studio .NET Control to generate, create barcode image in .NET applications. ANSI/AIM Code 39 Creator In Visual Studio .NET Using Barcode creation for .NET framework Control to generate, create Code 39 image in .NET applications. THE MULTIPLIER a that determines whether the processor of Fig. 348 is stable or unstable. The explanation is as follows. First remember that, in this case, x nT 0 for all time EXCEPT at t 0, when x nT 1. Thus the output at the instant t 0 is also 1. Then, following this, after T seconds has elapsed, a timedelayed signal, (1) a a, arrives at the input to the adder; thus, at t T, the output is a. Then, after another T seconds has elapsed, a timedelayed signal, now equal to a a a2 , arrives at the input to the adder, so that, at t 2T, the output is a2 . Then, after another T seconds has elapsed, a timedelayed signal, now equal to a3 , is fed back to the input to the adder, so that at t 3T the output is a3 . Continuing on in this way we see that, at any integral multiple of time T, t nT, the output is equal to an ; that is, in Fig. 348, y nT an . Thus the nature of the output sequence in Fig. 348 depends upon the value of the multiplier constant a. Let us discuss this in more detail, as follows. First, note that our de nition of stability or instability, as given above, could also be stated in the following equivalent way. Let a single unit pulse p nT be applied to the input of a (recursive) processor, and let y nT denote the value of the output at any time nT seconds later. Now let L denote the value that y nT would approach if n were allowed to become in nitely great (denoted by writing n ! 1, or loosely, for convenience, simply as n 1 ). We can then say that, in general, a processor is stable if L 0, but is unstable if L is not equal to zero. Let us apply this principle to Fig. 348, where we ve already found that y nT an 591 Code 128 Generation In .NET Framework Using Barcode creation for .NET framework Control to generate, create Code 128B image in VS .NET applications. Creating 2/5 Standard In .NET Using Barcode printer for .NET Control to generate, create Standard 2 of 5 image in Visual Studio .NET applications. Thus, applying the above rule to the particular processor of Fig. 348, we have that
Code 128 Code Set C Encoder In .NET Using Barcode drawer for Reporting Service Control to generate, create Code 128 Code Set A image in Reporting Service applications. Code 128A Decoder In C# Using Barcode scanner for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. lim y nT lim an L
USS128 Maker In Java Using Barcode maker for Java Control to generate, create UCC  12 image in Java applications. Bar Code Maker In Visual Basic .NET Using Barcode drawer for .NET Control to generate, create bar code image in .NET applications. 592 Scan EAN13 In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Make UPC Code In None Using Barcode encoder for Office Word Control to generate, create UPC Code image in Office Word applications. It s apparent that, in this case, the value of L will depend upon the value of the constant multiplier a. As a matter of fact, after some thought we realize that we must consider three separate possibilities for the value of a, these being the cases for a GREATER than 1, a EQUAL to 1, and a LESS than 1. Let us consider each of the three cases as follows. (a > 1): Here the values of the output samples, an , theoretically become in nitely great for n 1. Thus in this case L is certainly not equal to zero, so that Fig. 348 is unstable for a > 1. This is illustrated in Fig. 349. Case II. (a 1): Since 1n 1 we have that L 1, and thus Fig. 348 is unstable for a 1, as illustrated in Fig. 350. Case III. (a < 1): The integral power of a number less than 1 is less than the given number; for instance, if a 1=3, then a2 1=9; a3 1=27, and so on. Thus for this case L becomes equal to zero L 0 as n becomes in nitely great; hence Fig. 348 is stable for a < 1, as illustrated in Fig. 351. In regard to Fig. 349, the output of an actual processor could not, of course, become in nitely great ; instead, in such a case the output would cease increasing and stall when the maximum holding capacity of the digital circuits was exceeded. Now let s return to Fig. 348 and this time apply the ztransform. Let us begin by writing down the nTdomain equation for the gure, which, since it s given that x nT p nT , is y nT p nT ay nT T Case I. Paint Code 128 Code Set C In ObjectiveC Using Barcode maker for iPad Control to generate, create ANSI/AIM Code 128 image in iPad applications. Bar Code Maker In None Using Barcode creator for Font Control to generate, create bar code image in Font applications. 
