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313lecture2_signals - EE 313 Linear Systems and Signals...

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Signals and Signal Properties Prof. Adnan Kavak Dept. of Electrical and Computer Engineering The University of Texas at Austin EE 313 Linear Systems and Signals Fall 2008
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2-2 Signals Signal is a set of data or information, which is a function of an independent variable (time, space, etc) E.g. Phone or TV signal, monthly sales of corporation, daily stock price, daily temperature, etc. Continuous-time signals are functions of a real argument x ( t ) where t can take any real value x ( t ) may be 0 for a given range of values of t Discrete-time signals are functions of an argument that takes values from a disrete set x [ n ] where n {...-3,-2,-1,0,1,2,3...} We sometimes use “index” instead of “time” when discussing discrete-time signals Values for x may be real or complex
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2-3 Signal Energy For a real-valued signal For a complex-valued signal (To make sure that energy is real, use magnitude square) Measure of the signal size as the area under its amplitude square
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2-4 Comment: Why do we use amplitude square for energy? Instantenous power: p(t) = i(t) * v(t) (in general) f(t) = i(t) = v(t) [ Assuming 1 Ohm resistance] Then, instantenous power: p(t) = f(t) * f(t) This is why we use square of the signal amplitude (physical reason). Then, energy is integral of the instantenous power. Mathematically, if we didn’t use square of amplitude, then energy may be negative which doesn’t make any sense.
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2-5 Remarks about Signal Energy Signal energy is always positive Some signals (e.g. periodic) have infinite energy.
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