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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part3

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part3

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Chapter 1 Elementary Signals 1 2 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications We can express (1.3) by the waveform shown in Figure 1.2. Figure 1.2. Waveform for as defined in relation (1.3) The waveform of Figure 1.2 is an example of a discontinuous function. A function is said to be dis- continuous if it exhibits points of discontinuity, that is, the function jumps from one value to another without taking on any intermediate values. 1.2 The Unit Step Function A well known discontinuous function is the unit step function * which is defined as (1.4) It is also represented by the waveform of Figure 1.3. Figure 1.3. Waveform for In the waveform of Figure 1.3, the unit step function changes abruptly from to at . But if it changes at instead, it is denoted as . In this case, its waveform and definition are as shown in Figure 1.4 and relation (1.5) respectively. Figure 1.4. Waveform for * In some books, the unit step function is denoted as , that is, without the subscript 0. In this text, however, we will reserve the designation for any input when we will discuss state variables in Chapter 5. 0 v out v S t v out u 0 t ( ) u 0 t ( ) u t ( ) u t ( ) u 0 t ( ) 0 t 0 < 1 t 0 > = u 0 t ( ) 0 1 t u 0 t ( ) u 0 t ( ) 0 1 t 0 = t t 0 = u 0 t t 0 ( ) 1 t 0 0 u 0 t t 0 ( ) t u 0 t t 0 ( )
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