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Understanding Linear Time-Invariant Systems in Analog Signaling

Learn about eigenfunctions, amplitude response, phase shift, bandwidth, Sampling Theorem, signal reconstruction, noise power, information theory, and signaling capacity in analog signaling systems. This comprehensive guide explores the fundamental concepts and principles crucial for understanding linear time-invariant systems in signal processing.

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Understanding Linear Time-Invariant Systems in Analog Signaling

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  1. inputs are functions of time linear A linear time-invariant system is characterized by the eigenfunctions Analog Signaling gain phase transfer function A(w) = amplitude response – limits bandwidth Θ(w) = phase shift – distorts pulse shape limits signaling capacity Sampling Theorem: A band-limited signal of duration T and of bandwidth W can be reconstructed perfectly by 2WT samples, at evenly spaced intervals. The sample vector (x1, …, x2WT) can be viewed as a point in 2WT-dimensional space. A.9

  2. These samples can tell us the signal’s energy and their radius (distance from origin) And the signal power (energy per unit time) is The noise added to the channel has power N, and a corresponding radius The total power (signal + noise) has radius How many spheres of noise can fit in? # of messages The amount of information sent is And the rate of info is E.g. (telephone) Appendix (end.)

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