Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part43

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part43

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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 8 57 Copyright © Orchard Publications Solutions to End of Chapter Exercises fprintf(' \n'); fprintf('atan(6*pi) = %4.2f \t', atan(6*pi)); fprintf('atan(2*pi) = %4.2f', atan(2*pi)) atan(6*pi) = 1.52 atan(2*pi) = 1.41 and thus Therefore, the percentage of the input appearing at the output is 10 . First, we compute the total energy of the pulse in terms of . and since is an even function, Next, we denote the energy in the frequency interval as in the frequency domain we obtain W out 9 2 π ------ 1 2 -- ω 2 --- atan 4 π 12 π 9 4 π ------ 12 π 2 --------- atan 4 π 2 ------ atan 9 4 π ------ 6 π atan 2 π atan ( ) = = = W out 9 4 π ------ 1.52 1.41 ( ) 0.08 J = = W out W in ----------- 100 × 0.08 2.25 --------- 3.56% = = A u 0 t T + ( ) u 0 t T ( ) [ ] 2AT ω T sin ω T --------------- 0 ω T 2 π 2 π π −π A T T t 0 f t ( ) F ω ( ) f t ( ) W total f t ( ) 2 t d A 2 t d T T = = f t ( ) W total 2 A 2 t d 0 T 2A 2 t 0 T 2A 2 T = = = π T rad ω π T rad W out W out 1 2 π ------ F ω ( ) 2 ω d 1 2 π ------ 2AT ω T sin ω T --------------- 2 ω d π T π T = =
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