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Quiz4_sol

# Quiz4_sol - -1 1 1 f H(f-2 2 1 f X(f Solution The output of...

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ECEN 314 Solution to Quiz # 4 Georghiades November 30, 2009 Note: Quiz is open-book, 15 minutes long. 1. Consider a system whose frequency response H ( f ) is given in the figure below and a signal x ( t ) whose Fourier transform X ( f ) is also given in the figure. Compute the energy of the output of the system, y ( t ), when x ( t ) is applied at its input.
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Unformatted text preview: -1 1 1 f H(f)-2 2 1 f X(f) Solution The output of the system, Y ( f ) is Y ( f ) = X ( f ) H ( f ) . By Parseval’s theorem, the energy in the output is: E = Z ∞-∞ | Y ( f ) | 2 df = Z ∞-∞ | X ( f ) H ( f ) | 2 df = Z 1-1 | X ( f ) | 2 df = 2 Z 1 ± 1-1 2 f ² 2 df = 7 6 . 1...
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