Express the real part of each of the following signals in the form Ae-ar cos(wt + cp)

Chapter 1, Problem 1.8

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QUESTION:

Express the real part of each of the following signals in the form Ae-ar cos(wt + cp), where A, a, w, and cp are real numbers with A> 0 and -7r < cp ~ 'TT: (a) x 1 (t) = -2 (b) x2(t) = heJ1TI4 cos(3t + 27T) (c) x3(t) = e- 1 sin(3t + 'TT) (d) x4 (t) = je(-2-r JIOO)t

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QUESTION:

Express the real part of each of the following signals in the form Ae-ar cos(wt + cp), where A, a, w, and cp are real numbers with A> 0 and -7r < cp ~ 'TT: (a) x 1 (t) = -2 (b) x2(t) = heJ1TI4 cos(3t + 27T) (c) x3(t) = e- 1 sin(3t + 'TT) (d) x4 (t) = je(-2-r JIOO)t

ANSWER:

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In this problem we need to express the real part of the given signals in the form

Also given that  and  

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