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|a Karris, Steven T.
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|a Signals and systems :
|b with MATLAB Computing and Simulink modeling /
|c Steven T. Karris.
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|a 5th ed.
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|a Fremont :
|b Orchard Publications,
|c 2012.
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|a 1 online resource (671 pages)
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|a Preface Signals and Systems Fifth; Preface; TOC Signals and Systems Fifth; Chapter 01 Signals and Systems Fifth; Chapter 02 Signals and Systems Fifth; Chapter 2; The Laplace Transformation; his chapter begins with an introduction to the Laplace transformation, definitions, and properties of the Laplace transformation. The initial value and final value theorems are also discussed and proved. It continues with the derivation of the Laplac ... ; 2.1 Definition of the Laplace Transformation; The two-sided or bilateral Laplace Transform pair is defined as; (2.1); (2.2).
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|a Where denotes the Laplace transform of the time function, denotes the Inverse Laplace transform, and is a complex variable whose real part is, and imaginary part, that is, .In most problems, we are concerned with values of time greater than some reference time, say, and since the initial conditions are generally known, the two-sided Laplace transform pair of (2.1) and (2.2) simplifies to the unilateral or one-sided Lap ... ; (2.3); (2.4); The Laplace Transform of (2.3) has meaning only if the integral converges (reaches a limit), that is, if; (2.5).
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|a To determine the conditions that will ensure us that the integral of (2.3) converges, we rewrite (2.5) as(2.6); The term in the integral of (2.6) has magnitude of unity, i.e., and thus the condition for convergence becomes; (2.7); Fortunately, in most engineering applications the functions are of exponential order. Then, we can express (2.7) as, ; (2.8); and we see that the integral on the right side of the inequality sign in (2.8), converges if . Therefore, we conclude that if is of exponential order, exists if; (2.9); where denotes the real part of the complex variable.
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|a Evaluation of the integral of (2.4) involves contour integration in the complex plane, and thus, it will not be attempted in this chapter. We will see in the next chapter that many Laplace transforms can be inverted with the use of a few standard pai ... In our subsequent discussion, we will denote transformation from the time domain to the complex frequency domain, and vice versa, as; (2.10); 2.2 Properties and Theorems of the Laplace Transform; The most common properties and theorems of the Laplace transform are presented in Subsections 2.2.1 through 2.2.13 below.; 2.2.1 Linearity Property.
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|a The linearity property states that ifhave Laplace transforms; respectively, and; are arbitrary constants, then, ; (2.11); Proof:; Note 1:; It is desirable to multiply by the unit step function to eliminate any unwanted non-zero values of for .; 2.2.2 Time Shifting Property; The time shifting property states that a right shift in the time domain by units, corresponds to multiplication by in the complex frequency domain. Thus, ; (2.12); Proof:; (2.13); Now, we let ; then, and . With these substitutions and with, the second integral on the right side of (2.13) is expressed as.
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|a 2.2.3 Frequency Shifting Property.
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|a Written for junior and senior electrical and computer engineering students, this text is an introduction to signal and system analysis, digital signal processing, and the design of analog and digital filters. The text also serves as a self-study guide for professionals who want to review the fundamentals. The expanded fifth edition contains additional information on window functions, the cross correlation and autocorrelation functions, a discussion on nonlinear systems including an example that derives its describing function, as well as additional end-of-chapter exercises.
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|a Print version record.
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|a Includes bibliographical references and index.
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|a eBooks on EBSCOhost
|b EBSCO eBook Subscription Academic Collection - Worldwide
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|a Systems Analysis
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|i Print version:
|a Karris, Steven.
|t Signals and Systems : with MATLAB Copmputing and Simulink Modeling.
|d Fremont : Orchard Publications, ©2012
|z 9781934404232
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