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Unformatted text preview: CSE 3451 Final exam page 6 of 12 3. [20 points] Consider the nonlinear device described by the following relationship between the input ﬁt) and
output Mt)
EN) = 93(3) + 933(3) (3) Let the input 5:(t) be a sinusoidal signal
ﬁt) = A3 cos(wct) (4) with Ac and cum being constants. (a) (10 points) Determine the frequency content of y(t) by sketching the magnitude spectrum Y(jw) of
the CTFT of the output y(t). (b) (10 points) Describe the complete speciﬁcations of a system that extracts signal ﬁt) from y(t). +5%f_ 1' . n e (a) 91m ﬂew“ ﬁe = m)  Ceswcf :. 16+). 2
. . “L I; Ach— l A»! Aim. MM tat. I, CSE 3451 Final exam page 7 of 12 CSE 3451 Final exam page 8 of 12 4. [15 points] You are hired by a signal processing ﬁrm and you are hoping to impress them with the skills
that you have acquired in the Signals and Systems course. The ﬁrm asks you to design a discretetime (DT)
linear timeinvariant (LTI) system, which has the property that if the input is Ilkl = (1/3)”U[kl — (1/4)(1/2)’°_1U[lc *1la (5)
the output is given by
we] = {larva} (6)
(a) (5 points) Determine the transfer function ng1 of the DT LTI system that has the aforementioned
property. Ya; 92.. x (b) (5 points) Calculate the impulse rc onse [k] of the DT LTI system that you obtaned in (a). (c) (5 points) Find the difference equation relating :L'[k] and y[k] that characterizes the aforementioned
system. _ i l a
La) 'xcl‘i] X197) = ___1_ ~33 _ M CSE 3451 Final exam page 9 of 12 (1— €653) L F116”)
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 Fall '10
 A
 Digital Signal Processing, Signal Processing, LTI system theory

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