3 points suppose the input to the system is x n cos2

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Unformatted text preview: = 3 π A( 23 ) = π 3 π α( 23 ) = 14. [4 points]: Provide a careful and fully labeled sketch of A(Ω) below, for Ω in the interval [−π, π ]. 6.02 Fall 2012, Quiz 2 Page 11 of 17 15. [3 points]: Suppose the input to the system is x// [n] = cos(2π n + θ0 ) . Write down an explicit 3 expression for the corresponding output y // [n]. y // [n] = 16. [3 points]: Suppose the input to the system is now x/// [n] = cos(π n + θ0 ) . Write down an 3 explicit expression for the corresponding output y /// [n]. y /// [n] = 17. [2 points]: For the special case of θ0 = 0 in the preceding two problems, show that you recover the results you obtained in the last section (Problems 8 and 9). If you don’t, then you have some checking (or explaining!) to do. Page 12 of 17 6.02 Fall 2012, Quiz 2 IV Spectre in the Mirror Given a real signal x[·] with DTFT ∞ 0 X (Ω) = x[m]e−j Ωm = |X (Ω)|ej ∠X (Ω) , m=−∞ let v [·] denote the signal obtained by time-reversing x[·], so v [n] = x[−n]. 18. [4 p...
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.02 at MIT.

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