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barcode print in asp net PROPERTIES OF CONTINUOUSTIME LTI SYSTEMS . in .NET framework
23 PROPERTIES OF CONTINUOUSTIME LTI SYSTEMS . Decoding Denso QR Bar Code In .NET Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET applications. QR Code 2d Barcode Maker In Visual Studio .NET Using Barcode printer for .NET Control to generate, create QR Code image in VS .NET applications. Systems with or without Memory: Decoding QRCode In .NET Using Barcode recognizer for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Barcode Creation In .NET Framework Using Barcode creation for Visual Studio .NET Control to generate, create bar code image in VS .NET applications. Since the output y(t) of a memoryless system depends on only the present input x(t), then, if the system is also linear and timeinvariant, this relationship can only be of the form Barcode Recognizer In VS .NET Using Barcode recognizer for .NET framework Control to read, scan read, scan image in VS .NET applications. Encode QR Code 2d Barcode In Visual C# Using Barcode maker for .NET framework Control to generate, create Quick Response Code image in .NET applications. (2.14) Y ( [ )= Kx(t) where K is a (gain) constant. Thus, the corresponding impulse response h(f) is simply h ( t ) = K6(t) Therefore, if h(tJ Printing QR Code JIS X 0510 In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create QRCode image in ASP.NET applications. Generating QR Code JIS X 0510 In Visual Basic .NET Using Barcode generator for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications. (2.15) Printing Data Matrix ECC200 In .NET Framework Using Barcode creation for VS .NET Control to generate, create Data Matrix ECC200 image in .NET applications. Barcode Creator In .NET Framework Using Barcode creation for Visual Studio .NET Control to generate, create bar code image in .NET applications. 0 for I,, Make GS1  12 In .NET Framework Using Barcode printer for .NET framework Control to generate, create UPCA image in .NET framework applications. ISSN  13 Creation In Visual Studio .NET Using Barcode creator for Visual Studio .NET Control to generate, create International Standard Serial Number image in VS .NET applications. 0, the continuoustime LTI system has memory.
ECC200 Generation In ObjectiveC Using Barcode printer for iPad Control to generate, create ECC200 image in iPad applications. EAN13 Supplement 5 Generation In ObjectiveC Using Barcode creation for iPhone Control to generate, create EAN13 image in iPhone applications. B. Causality: GTIN  12 Drawer In Java Using Barcode encoder for Eclipse BIRT Control to generate, create GTIN  12 image in BIRT reports applications. Generate Universal Product Code Version A In None Using Barcode maker for Software Control to generate, create UPC Code image in Software applications. As discussed in Sec. 1.5D, a causal system does not respond to an input event until that event actually occurs. Therefore, for a causal continuoustime LTI system, we have Bar Code Drawer In VS .NET Using Barcode creation for ASP.NET Control to generate, create barcode image in ASP.NET applications. Bar Code Creator In None Using Barcode generator for Excel Control to generate, create bar code image in Microsoft Excel applications. Applying the causality condition (2.16) to Eq. (2.101, the output of a causal continuoustime
Data Matrix Decoder In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. UPC  13 Creation In Java Using Barcode creation for BIRT Control to generate, create EAN13 image in BIRT applications. CHAP. 21
LINEAR TIMEINVARIANT SYSTEMS
LTI system is expressed as
Alternatively, applying the causality condition ( 2.16) to Eq. (2.61, we have y(t) = lt x ( r ) h ( t  T )d r w
(2.18) Equation (2.18) shows that the only values of the input x ( t ) used to evaluate the output y( t ) are those for r 5 t. Based on the causality condition (2.161, any signal x(t) is called causal if and is called anticausal if x(t) = 0 t>O Then, from Eqs. (2.17), (2. I8), and (2. Iga), when the input x ( t ) is causal, the output y(t ) of a causal continuoustime LTI system is given by C. Stability: The BIBO (boundedinput/boundedoutput)stability of an LTI system (Sec. 1.5H) is readily ascertained from its impulse response. It can be shown (Prob. 2.13) that a continuoustime LTI system is BIBO stable if its impulse response is absolutely integrable, that is, 2.4 EIGENFUNCTIONS OF CONTINUOUSTIME LTI SYSTEMS In Chap. 1 (Prob. 1.44) we saw that the eigenfunctions of continuoustime LTI systems represented by T are the complex exponentials eS',with s a complex variable. That is, where h is the eigenvalue of T associated with e"'. Setting x(t) = es' in Eq. (2.10), we have where Thus, the eigenvalue of a continuoustime LTI system associated with the eigenfunction es' is given by H ( s ) which is a complex constant whose value is determined by the value of s via Eq. (2.24). Note from Eq. (2.23) that y(0) = H ( s ) (see Prob. 1.44). The above results underlie the definitions of the Laplace transform and Fourier transform which will be discussed in Chaps. 3 and 5. LINEAR TIMEINVARIANT SYSTEMS
[CHAP. 2
SYSTEMS DESCRIBED BY DIFFERENTIAL EQUATIONS Linear ConstantCoefficient Differential Equations: A general Nthorder linear constantcoefficient differential equation is given by
where coefficients a , and b, are real constants. The order N refers to the highest derivative of y ( 0 in Eq. (2.25).Such differential equations play a central role in describing the inputoutput relationships of a wide variety of electrical, mechanical, chemical, and biological systems. For instance, in the RC circuit considered in Prob. 1.32, the input x ( 0 = il,(O and the output y ( l ) = i,.(t)are related by a firstorder constantcoefficient differential equation [Eq. ( l . 1 0 5 ) ] The general solution of Eq. (2.25) for a particular input x ( t ) is given by
where y , ( t ) is a particular solution satisfying Eq. (2.25) and y h ( t ) is a homogeneous solution (or complementary solution) satisfying the homogeneous differential equation The exact form of y h ( t )is determined by N auxiliary conditions. Note that Eq. ( 2 . 2 5 )does not completely specify the output y ( t ) in terms of the input x ( t ) unless auxiliary conditions are specified. In general, a set of auxiliary conditions are the values of at some point in time.
B. Linearity: The system specified by Eq. (2.25) will be linear only if all of the auxiliary conditions are zero (see Prob. 2.21). If the auxiliary conditions are not zero, then the response y ( t ) of a system can be expressed as where yzi(O,called the zeroinput response, is the response to the auxiliary conditions, and yz,(t), called the zerostate response, is the response of a linear system with zero auxiliary conditions. This is illustrated in Fig. 22. 0 Note that y,,(t) # y h ( t ) and y,,(t) 2 y,(t) and that in general yZi( contains y h ( t ) and y,,( t ) contains both y h ( t and y,( t (see Prob. 2.20).

