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Fa+2004+Ch+1+lecture+1

Fa+2004+Ch+1+lecture+1 - Linear Systems and Signals Lecture...

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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, 2-D pictures {x,y}, 3-D 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

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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 2 ( ) x E x t dt −∞ = Generalized for complex signals: 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 Æ 0 as |t| Æ 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.