Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part27

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part27

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Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth Edition 6 19 Copyright © Orchard Publications Circuit Analysis with the Convolution Integral Figure 6.32. Formation of for Example 6.7 Figure 6.33 shows the formation of . Figure 6.33. Formation of for Example 6.7 Figure 6.34 shows the convolution . Figure 6.34. Convolution of for Example 6.7 Therefore, for the interval , we obtain (6.35) and the convolution is shown in Figure 6.35. 1 0 u 0 τ () τ u 0 τ u 0 t τ 1 t 0 u 0 t τ τ u 0 t τ u 0 t h t 1 0 t τ h τ u 0 t *h t 0t << u 0 t *h t u 0 t τ h τ ()τ d 1 e t τ d 0 t e t 0 t e t t 0 1e t u 0 t == = = = u 0 t *h t
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Chapter 6 The Impulse Response and Convolution 6 20 Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth Edition Copyright © Orchard Publications Figure 6.35. Convolution of for Example 6.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 1e t () u 0 t u 0 t ht
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Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth Edition 6 21 Copyright © Orchard Publications Summary 6.6 Summary The impulse response is the output (voltage or current) of a network when the input is the delta function. The determination of the impulse response assumes zero initial conditions. A function is an even function of time if the following relation holds. A function is an odd function of time if the following relation holds. The product of two even or two odd functions is an even function, and the product of an even function times an odd function, is an odd function.
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This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part27

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