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Unformatted text preview: EE 3120 Linear Signals and Systems Chapter 1 Introduction to Signals and Systems Linear Systems and Signals Lecture 1 Introduction to signals and systems Signals: single valued functions that carry information (e.g. voice, radar, control, heart EKG, brainwaves, 2D pictures {x,y}, 3D video or RF electromagnetic radiation {x,y,t}) Systems: perform some kind of manipulation (processing) of signals (e.g. microphone, speaker, amplifier, demodulator) Systems can be electrical, mechanical, hydraulic, etc. Continuous time signals signals defined at every instant in time. Usually denoted f(t) for all t (,). In reality, no signal starts from  and lasts forever but it is convenient to represent signals this way. Discrete time signals signals defined only at discrete instants of time, but have a continuous range of amplitudes Digital signals discrete time signals with discrete (quantized) amplitudes Size of a Signal Many times engineers are interested in quantifying a signal. The two most common ways of quantifying a signal is by computing the signal energy and signal power. 2 ( ) x E x t dt = Signal Energy Defined as the area under squared signal, or the magnitude squared area. This is only a meaningful measure of the signal size if it is finite. These integrals will be finite only if the signal amplitude 0 as t infinity. If a signal amplitude does not eventually decay to zero, then the signal energy is infinite and the signal is NOT an energy signal. 2 ( ) x E x t dt = Generalized for complex signals: Signal Power 2 2 2 1 lim ( ) T x T T P x t dt T = 2 2 2 1 lim ( ) T x T T P x t dt T = Generalized for complex signals: If the signal energy is infinite, we can calculate another measure of the signal, the time average of the energy, or the power of the signal. The signal power is the time average or mean of the signal amplitude squared. The square root of this signal power is the rootmeansquared, or RMS of a signal. The signal power can be found as long as the signal is periodic, otherwise the average may not exist. Size of a Signal The energy calculated does not indicate the actual energy signal because the energy also depends on the load. We can interpret the measurement as the energy dissipated across a normalized load of a 1ohm resistor. x(t) 1 ohm x(t) R2 R1 A real signal source consists of an independent voltage source and a series resistance. The energy delivered to R2 depends on R1 and R2 through voltage division. We use the normalization to represent the maximum energy capability....
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 Fall '08
 ARAVENA

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