Signal Processing and Linear Systems-B.P.Lathi copy

However e quating t he coefficients of 8 1 a nd 8 0

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Unformatted text preview: operate by t he laws of Newton a nd Laplace t o t he end of time. 3 Laplace presented a copy o f Mechanique Celeste t o Napoleon, who, after reading t he book, took Laplace to t ask for n ot including God in his scheme: "You have written this huge book on t he s ystem of t he world without once mentioning t he a uthor of t he universe." "Sire," Laplace retorted, "I h ad no need of t hat hypothesis." Napoleon was not amused, a nd w hen he reported this reply t o Lagrange, t he l atter remarked, "Ah, b ut t hat is a fine hypothesis. I t explains so many things." 4 Napoleon, following his policy of honoring a nd p romoting scientists, made Laplace t he m inister of t he interior. To Napoleon's dismay, he found t he g reat mathematician-astronomer bringing " the s pirit of infinitesimals" into a dministration, a nd so had Laplace transferred hastily to t he s enate. Oliver Heaviside ( 1850-1925) A lthough Laplace published his transform method t o solve differential equations in 1779, t he m ethod did not catch on until a century later. I t was rediscovered independently in a r ather awkward form by a n eccentric British engineer, Oliver Heaviside (1850-1925), one of t he t ragic figures in t he h istory of electrical engineering. Despite his prolific contributions t o electrical engineering, he was severely criticized during his lifetime, a nd was neglected later to t he p oint t hat h ardly a 380 6 Continuous-Time System Analysis Using t he Laplace Transform P .S. d e L aplace ( left) a nd O liver H eaviside ( right). t extbook t oday mentions his name o r c ontributions. W ith t he passage of time, Heaviside becomes more distant, although his studies had a major impact on many aspects of m odern electrical engineering. I t was Heaviside who made transatlantic communication possible by inventing cable loading, b ut no one ever mentions him as a pioneer o r a n innovator in telephony. I t was Heaviside who suggested t he use of inductive c able loading, b ut t he c redit is given t o M. P upin, who actually built 5 t he first loading coil. In addition, Heaviside was • T he f irst t o find a solution t o t he distortionless transmission line; • T he i nnovator of lowpass filters; • T he f irst t o w rite Maxwell's equations in modern form; • T he co-discoverer of r ate energy transfer by a n electromagnetic field; • An e arly champion of the now-common phasor analysis; • An i mportant c ontributor to the development of vector analysis. In fact, he 6 essentially created t he s ubject independently of Gibbs ; • An originator of t he use of operational mathematics used t o solve linear integro-differential equations, which eventually led to rediscovery of t he ignored Laplace transform; • T he f irst t o theorize (along with Kennelly of Harvard) t hat a c onducting layer (the Kennelly-Heaviside layer) of atmosphere exists, which allows radio waves t o follow e arth's c urvature instead of tr...
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