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Unformatted text preview: of time, and the other is an odd function of
time. Which is which? Circle the correct answer below and show your reasoning. (Recall that f [n] is
called an even function if f [−n] = f [n]; it is called an odd function if f [−n] = −f [n].) x1 [n] is Odd / Even x2 [n] is Odd / Even The above decomposition is unique (we don’t ask you to show that, though it’s not hard) — i.e., there is no
other decomposition of an arbitrary signal into the sum of an even part and an odd part.
23. [4 points]: Denote the DTFTs of the above signals x1 [n] and x2 [n] by X1 (Ω) and X2 (Ω)
respectively. One of these DTFTs is purely real and the other one is purely imaginary. Which is
which? Circle the correct answer and show your reasoning. X1 (Ω) is Real / Imaginary X2 (Ω) is Real / Imaginary 6.02 Fall 2012, Quiz 2 Page 15 of 17 It follows from the answers to the previous two problems that the real part of X (Ω) equals either X1 (Ω) or
X2 (Ω) — you will know which from your answers above. Thus the Q Branch wizards can inverse trans...
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.02 at MIT.
 Fall '12
 GeorgeVerghese

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