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Unformatted text preview: xplain! Vth will have to be Increased / Decreased / Unchanged Page 5 of 17 6.02 Fall 2012, Quiz 2 II Signals and Systems Consider the signal x[n] given by n
x[n] = cos(2π )
3 π
for all n. A segment of the signal, for n in the interval [−3, 3], is shown below. (Note that cos( 23 ) = −0.5.) Figure 1: Input signal x[n]. 7. [3 points]: What is the angular frequency Ω0 , in radians/sample, of this sinusoidal signal x[n]?
And what is its period? Ω0 = Period = Suppose the above sinusoidal signal x[n] is used as the input to an LTI system whose unit sample response
is
h[n] = δ [n] − δ [n − 1] + δ [n − 2] ,
where δ [n] as usual denotes the unit sample function. A plot of h[n] for n in [−3, 3] is shown on the next
page. Page 6 of 17 6.02 Fall 2012, Quiz 2 Figure 2: Unit sample response h[n] of LTI system.
8. [6 points]: Determine the output y [n] of the system for n = 0, 1, 2, showing your computations
explicitly. y [0] = , y [1] = , y [2] = Now suppose instead that we use a sinusoidal input that has half the frequency of the preceding case. This
input, which we’ll denote by x/ [n], is given fo...
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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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