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# hw7sol - 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 Problem 1: 15 points a.) ? ? = ???? 2 𝜋𝑓 1 ? ∗ ???? 2 𝜋𝑓 2 ? = ?? 2 [cos 2 𝜋 𝑓 1 + 𝑓 2 ? + cos 2 𝜋 𝑓 1 − 𝑓 2 ? ] , with frequencies f 1 +f 2 & f 1 -f 2 b.) ? ? = ???? 2 𝜋𝑓 1 ? ∗ ???? 2 𝜋𝑓 1 ? = ?? 2 cos 2 𝜋 2 𝑓 1 ? , with frequency 2f 1 c.) ? ? = ???? 2 𝜋𝑓 1 ? ∗ ??𝑖? 2 𝜋𝑓 2 ? = ?? 2 [sin 2 𝜋 𝑓 1 + 𝑓 2 ? − sin 2 𝜋 𝑓 1 − 𝑓 2 ? ] , with frequencies f 1 +f 2 & f 1 -f 2 d.) ? ? = ??𝑖? 2 𝜋𝑓 1 ? ∗ ??𝑖? 2 𝜋𝑓 2 ? = ?? 2 [cos 2 𝜋 𝑓 1 − 𝑓 2 ? − cos 2 𝜋 𝑓 1 + 𝑓 2 ? ] , with frequencies f 1 +f 2 & f 1 -f 2 e.) ? ? = ???? 2 𝜋𝑓 1 ? + ???? 2 𝜋𝑓 2 ? ∗ ???? (2 𝜋𝑓 3 ? ) = ?? 2 [cos 2 𝜋 𝑓 1 + 𝑓 3 ? + cos 2 𝜋 𝑓 1 𝑓 3 ? ] + ?? 2 [cos 2 𝜋 𝑓 2 + 𝑓 3 ? + cos 2 𝜋 𝑓 2 − 𝑓 3 ? ] , with frequencies f 1 +f 3 , f 1 -f 3 , f 2 +f 3 & f 2 -f 3 Problem 2: 20 points a.) Plot of M(f) b.) Plot of S(f) f1,A1/2 f2,A2/2 f3,A3/2 0 1 2 3 0 1 2 3 Amplitude Frequency

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c.) The bandwidth is 2*f 3 d.) The recovery of m(t) from s(t) is ? ? = ?𝑃𝐹 2 ? ? cos 2 𝜋𝑓 ? ? ∗ ? ? where LPF{} is a low pass filter to remove the 2*f c terms with a cutoff frequency between f 3 and 2*f c -f 3 .
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hw7sol - Carnegie Mellon University Department of...

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