Will the real impulse δ ( t ) please step ∫ t δ ( t ) dt up ?
نویسنده
چکیده
Abstract I seems to be widely believed that the Fourier and Laplace transforms are simply related to each other. Nothing could be further from the truth. The Fourier transform is the basis for the Hilbert vector-space expansion of signals. The Laplace transform is the basis of system functions, that are causal. The Fourier transform does not naturally include the step function, which must be shoe-horned into the theory. The Laplace transform naturally includes the step function, and thus the delta function, with out the need to introduce distributions. In fact we argue that the theory of distributions may be fundamentally flawed.
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