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Unformatted text preview: 1 Continuous Time Signals (Textbook Section 1.1) These overheads were originally developed by Mark Fowler at Binghamton University, State University of New York. 2 ContinuousTime Signals The mathematical model for a CT signal is a function of time. A CT signal is defined on the continuum of time values, e.g., f ( t ) for t Real line f ( t ) t Example: Example: 4 ContinuousTime Signals in Matlab The signal is sampled at a sufficiently high level of detail. Matlab interpolates the samples when graphed. (Figure 1.10 in textbook) % Figure 1.10 t=0:0.1:30; x = exp(.1*t).*sin(2/3*t); plot(t,x) grid axis([0 30 1 1]); ylabel('x(t)') xlabel('Time (sec)') title('Figure 1.10') x t = e 0.1t sin 2 3 t u t 5 Unit Step Function u ( t ) u t = { 1, t 0, t . . . u ( t ) 1 t Note: A step of height A can be made from Au ( t ) Step and Ramp Functions These are common textbook signals but are also common test signals, especially in control systems. . . . In system analysis, what use are unit step functions? 6 The unit step signal can model the act of switching on a power source V s R + C t = 0 R V s u ( t ) C + 7 Matlab and the Unit Step This is available as the heaviside function in some versions of Matlab. Here is an example: function y = heaviside(x) y = double(x >= 0); This will return a 1 when the argument is 0. Some implementations will return 0.5, and some will return NaN! 8 Unit Ramp Function r ( t ) Note: A ramp with slope m can be made from: mr ( t ) . . . r ( t ) 1 t 1 Unit slope r t = { t , t 0, t mr t = { mt , t 0, t 9 Relationship between u ( t ) & r ( t ) What is ? Depends on t value function of t : f ( t ) What is f ( t )? Write unit step as a function of  Integrate up to = t How does area change as t changes? i.e., Find Area u ( ) 1 = t Area = f ( t ) Running Integral of step = ramp t u d f t = t u d f t = t u d = 1 t = t = r t r t = t u d 10 Also note: For we have: Overlooking this, we can roughly say . . ....
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This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.
 Fall '10
 DRTERRENCETODD

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