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Twosided Laplace Transforms with Simple Applications
Foundations of Operational Analysis
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amplifier amplitude antenna applications arbitrary area transform assumed axis bandpass bandpass function bandwidth bounded variation Chap chapter circuit complex filtering complex numbers complex-valued function conjugate linear consider constant continuous convolution theorem corresponding course defined definition denote derivative differential equation discrete dominated dominated convergence theorem example exists exponential finite intervals Fourier transform frequency response given goes to zero hence Hilbert transform impulse response input integrand inverse transform inversion formula jumps Laplace transforms Lebesgue left half plane Lemma limit linear time-invariant systems mathematical mean-square modulation noise nonnegative obtain operational analysis output phase response poles power-density spectrum problem proof pulse radar rational function real bandpass real numbers real variable real-valued Recall Riemann integration sequence shown in Figure signal specific step response Stieltjes Stieltjes integral Suppose synthesis theory tion transfer function turn two-sided Laplace transform