Paul A. Lynn (auth.)'s An Introduction to the Analysis and Processing of Signals PDF

By Paul A. Lynn (auth.)

ISBN-10: 0333340302

ISBN-13: 9780333340301

ISBN-10: 1349860549

ISBN-13: 9781349860548

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Additional resources for An Introduction to the Analysis and Processing of Signals

Sample text

He became Governor of Lower Egypt and contributed many scientific papers to the Egyptian Institute which Napoleon founded, but when the French army capitulated in 1801 he returned to France and was made Prefect of the Department of Grenoble. He continued his scientific researches and in 1&22 published his monumental work Theone analytique de ia chaleur, in which he evolved the series which bears his name. Originally applied to the analysis of heat flow, the series has since been used in many branches of applied science, and constitutes one of the principal tools of signal analysis.

A fOG [(t'). e -(i/a). t'. G(s/a) . o 53 APERIODIC SIGNALS Time-shift Next, suppose that the function f(t) is shifted forward in time by an amount To. Whereas it was initially zero for t < 0, it is now zero for t < To. Hence its Laplace transform is given by j f(t- To) e-st. dt G 2 (s) = To Replacing (t - To) by t', we have G 2 (s) = j f(t'). exp {-s(t' + To)}· dt' = expJ -sTo)· ff(t'). exp (-st'). dt' 0 o = exp( -sTo). G(s) Frequency-shift Suppose next that the time functionf(t) is multiplied by the exponential term e -at.

10 ,-- (a) The unit step function, and (b) an exponentially decaying step function meet this latter condition, and strictly speaking do not therefore possess Fourier transforms. Fortunately, however, it is possible to consider them as limiting cases of waveforms which do possess transfonns. For example, we may evaluate the Fourier transform of a sine or cosine wave which exists only in the interval - T < t < T: we then allow T to become very large and in the limit approach the transform of the continuous function itself2.

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An Introduction to the Analysis and Processing of Signals by Paul A. Lynn (auth.)

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