Abstract
The Laplace transform is a generalization of the Fourier transform of a continuous time signal. The Laplace transform converges for signals for which the Fourier transform does not. Hence, the Laplace transform is a useful tool in the analysis and design of continuous time systems. This chapter introduces the bilateral Laplace transform , the unilateral Laplace transform, the inverse Laplace transform, and properties of the Laplace transform. Also, in this chapter, the LTI systems, including the systems represented by the linear constant coefficient differential equations, are characterized and analyzed using the Laplace transform. Further, the solution of state-space equations of continuous time LTI systems using Laplace transform is discussed.
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Further Reading
Doetsch, G.: Introduction to the theory and applications of the Laplace transformation with a table of Laplace transformations. Springer, New York (1974)
LePage, W.R.: Complex variables and the Laplace transforms for engineers. McGraw-Hill, New York (1961)
Oppenheim, A.V., Willsky, A.S.: Signals and systems. Prentice-Hall, Englewood Cliffs (1983)
Hsu, H.: Signals and systems, 2nd edn. Schaum’s Outlines, Mc Graw Hill (2011)
Kailath, T.: Linear systems. Prentice-Hall, Englewood Cliffs (1980)
Zadeh, L., Desoer, C.: Linear system theory. McGraw-Hill, New York (1963)
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Rao, K.D. (2018). Laplace Transforms. In: Signals and Systems. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68675-2_4
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DOI: https://doi.org/10.1007/978-3-319-68675-2_4
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Publisher Name: Birkhäuser, Cham
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Online ISBN: 978-3-319-68675-2
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