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# hwset7 - Carnegie Mellon University Department of...

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Carnegie Mellon University Department of Electrical and Computer Engineering 18-100 Fall 2009 Introduction to Electrical and Computer Engineering Homework 7 - Due Tuesday, October 27, 2008 Note: Exam II will take place during the lecture period on Thursday, Oct. 29. This set will not be graded prior to the exam, so if you would like to compare your solutions for this set with ours, you might want to photocopy your solutions prior to turning them in. There is no chapter in the Rizzoni text on Signal Processing. 1. Using trig identities from a calculus book or other, write out the results to the following modulations. State which frequencies exist in the signal s(t). a) s(t) = Acos( f 1 t) * Bcos( f 2 t) b) s(t) = Acos( f 1 t) * Bcos( f 1 t) c) s(t) = Acos( f 1 t) * Bsin( f 2 t) d) s(t) = Asin( f 1 t) * Bsin( f 2 t) e) s(t) = (Acos( f 1 t) + Bcos( f 2 t))* Kcos( f 3 t) 2. Suppose we have a signal that is made up of a sum of three frequencies: m(t) = A 1 cos( f 1 t) + A 2 cos( f 2 t) + A 3 cos( f 3 t) and that f 3 > f 2 > f 1 . Now suppose we modulate m(t) by multiplying it by a signal A c cos( f c

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