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barcode print in asp net System in .NET
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Code39 Decoder In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. UCC.EAN  128 Maker In ObjectiveC Using Barcode creator for iPhone Control to generate, create EAN / UCC  13 image in iPhone applications. Linear TimeInvariant Systems
Barcode Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Scanning Data Matrix In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. 2.1 INTRODUCTION
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A. Impulse Response: The impulse response h(t) of a continuoustime LTI system (represented by T) is defined to be the response of the system when the input is 6(t), that is, Response to an Arbitrary Input: From Eq. (1.27) the input x ( t ) can be expressed as
Since the system is linear, the response y( t of the system to an arbitrary input x( t ) can be expressed as Since the system is timeinvariant, we have Substituting Eq. (2.4) into Eq. (2.31, we obtain
CHAP. 21
LINEAR TIMEINVARIANT SYSTEMS
Equation (2.5) indicates that a continuoustime LTI system is completely characterized by its impulse response h( t 1. C. Convolution Integral: Equation (2.5) defines the convolution of two continuoustime signals x ( t ) and h ( t ) denoted by
Equation (2.6) is commonly called the convolution integral. Thus, we have the fundamental result that the output of any continuoustime LTI system is the convolution of the input x ( t ) with the impulse response h ( t ) of the system. Figure 21 illustrates the definition of the impulse response h ( t ) and the relationship of Eq. (2.6). Fig. 21 Continuoustime LTl system.
D. Properties of the Convolution Integral: The convolution integral has the following properties. I . Commutative: ~ ( t h ( t ) = h ( t )* ~ ( t ) *) 2. Associative: { x P )* h l ( 4 * h , ( t ) = x ( t )* { h l ( f * h 2 ( 4 ) 3. Distributive: x ( t ) * { h , ( t ) ) h N = x ( t )* h l ( t ) + x ( t )* h , ( t ) + E. Convolution Integral Operation: Applying the commutative property (2.7) of convolution to Eq. (2.61, we obtain (2.10) h ( r ) x ( t r ) d r m which may at times be easier to evaluate than Eq. (2.6). From Eq. ( 2 . 6 ) we observe that the convolution integral operation involves the following four steps: ( t )= h
)* x
1. The impulse response h ( ~ is timereversed (that is, reflected about the origin) to ) obtain h(  7 ) and then shifted by t to form h ( t  r ) = h [  ( r  t ) ]which is a function of T with parameter t. 2. The signal x ( r ) and h ( t  r ) are multiplied together for all values of r with t fixed at some value. LINEAR TIMEINVARIANT SYSTEMS
[CHAP. 2
3. The product x ( ~ ) h ( T ) is integrated over all T to produce a single output value t At). 4. Steps 1 to 3 are repeated as I varies over  03 to 03 to produce the entire output y( t ). Examples of the above convolution integral operation are given in Probs. 2.4 to 2.6.
F. Step Response: The step response s(t) of a continuoustime LTI system (represented by T) is defined to be the response of the system when the input is 4 1 ) ; that is, In many applications, the step response d t ) is also a useful characterization of the system. The step response s ( t ) can be easily determined by Eq. (2.10); that is, Thus, the step response s(t) can be obtained by integrating the impulse response h(t). Differentiating Eq. (2.12) with respect to t, we get Thus, the impulse response h ( t ) can be determined by differentiating the step response dl).

