Lesson_250

# Lesson_250 - EEL 3135: Dr. Fred J. Taylor, Professor Lesson...

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EEL 3135: Dr. Fred J. Taylor, Professor Lesson Title: Continuous-Time Signal and Systems Lesson Number: 25 (Section 9-1 to 9-4) Background: Continuous-time signals and systems are known to the general public as analog signals and systems. They have always been a part of man’s natural world in which our analog sensory systems are presumed to process analog signals. A bridge between discrete-time signal and system domains, studied to this point (Chapters 1-8), has been constructed using the Sampling Theorem, z-transforms, and similar tools. They are, however, differences between continuous- and discrete-time signal and system models that should be understood. The studies presented in Chapter 9 develop these ideas and builds a framework in which the study of continuous-time signal and systems can take place. Continuous-Time Signals: Continuous-time signals x(t) persist over an interval of time called the signal’s support . This interval of time can be finite (t [t 1 ,t 2 ]), one-side (t [0, ], also called “right sided”), or two-sided (t [- , ]). Over the signal’s support, the continuous-time signal is continuously resolved in time and amplitude (meaning that the time and amplitude values of x(t) are known with infinite precision). Over their support, continuous-time signals maybe deterministic (e.g., sinewave), random (e.g., noise) or arbitrary . They maybe 1- dimensional (e.g., x(t)=speech), 2- dimensional (e.g., x(k 1 ,k 2 )=2-D image), or multi- dimensional (e.g., x(k 1 , … , k n ) = mechanical system with n-degrees of freedom). Signals may also be real (e.g., A cos( ϖ 0 t)) or complex (e.g., Ae j ϖ 0 t ). Two-Sided Signals: Two-sided are assumed to exist for all time. For example, a common sinusoidal test signal: x 1 (t)=cos( ϖ 0 t), t [- , ] 1. can be used to mathematically study the dynamic behavior of continuous-time systems. The signal model assumes that the signal has always been present and will always be present. This raises questions of physical realizably which are often ignored. Two-sided signals can also be periodic (i.e., x(t)=x(t+kT 0 ), a property that a one-side or finite support signal can not mathematically possess. One-Sided Signals: One-sided signals are generally assume to be right sided ((t [0, ]). For example, a common test signal shown below: 1

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EEL 3135: Dr. Fred J. Taylor, Professor X 2 (t)=cos( ϖ 0 t), t [0, ] 2. It is assumed to be produce by a signal generator that was physically turned on at t=0. Unlike the two-sided sinusoid, this signal model does not raise any physical realizably questions. The signal describe by Equation 2 can also be mathematically represented in terms of the two-side signal found in Equation 1 and a continuous-time
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## This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

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Lesson_250 - EEL 3135: Dr. Fred J. Taylor, Professor Lesson...

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