Quiz1Soln

Quiz1Soln - Name: ECE 301: Quiz 1 Purdue University, Summer...

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Unformatted text preview: Name: ECE 301: Quiz 1 Purdue University, Summer 2009 1. Given x(t) as plotted below, plot 4x(2t − 3). Make sure to label your axes. 1.5 1 x(t) 0.5 0 −0.5 −1.5 −1 −0.5 0 t 0.5 1 1.5 Solution: 4 3 4x(2t−3) 2 1 0 −1 0 t 1 2 2. Let the signal y (t) = cos t + j sin t. Compute ∞ E∞ = −∞ |y (t)| dt 2 and P∞ 1 = lim T →∞ 2T T |y (t)|2dt −T Solution: We have that |y (t)| = | cos t + j sin t| = ∞ cos2 t + sin2 t = 1 ∞ E∞ = −∞ |y (t)|2dt = −∞ T −T 2 12 dt = ∞ T −T P∞ 1 = lim T →∞ 2T 1 |y (t)| dt = lim T →∞ 2T 12 dt = lim 2T =1 T →∞ 2T ...
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