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Unformatted text preview: gently to send to MI6 in London a signal x[n] that is 0 for
n < 0 and whose values for n ≥ 0 contain vital information. To prevent the casino from snooping, Mr.
Bond decides to instead transmit the DTFT X (Ω) of this signal (actually samples of the DTFT at points in
the interval [−π, π ], computed using his Furiously Fast Transformer, but we shall assume these samples are
so close together that he’s effectively transmitting the DTFT itself). Unfortunately, what gets transmitted
is just the real part of X (Ω). We’ll lead you through how the Q Branch wizards at MI6 (some of whom
are reported to have studied at MIT on the Cambridge-MIT Exchange) reconstructed x[n] from just this
information, and using the knowledge that x[n] = 0 for n < 0.
Any signal x[n] can be written as the sum of two terms:
x[n] = x[n] + x[−n]
x[n] − x[−n]
x1 [n] x2 [n] As indicated above, we shall call the ﬁrst term x1 [n] and the second term x2 [n].
22. [4 points]: Either x1 [n] or x2 [n] is an even function...
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- Fall '12