# Modulation - Signals and Systems - Exam, Exams for Signals and Systems Theory. Biju Patnaik University of Technology, Rourkela

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Main points of this exam paper are: Modulation, Omega, Noting Maximum Amplitudes, Center Frequencies, Frequency, First Zero Crossing, Labelling Important
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EE 120, Midterm #2, Fall 1994

EE 120, Midterm #2, Fall 1994

EE 120 Fall 1994 Midterm #2

Professor Fearing

Problem #1 (10 points)

A modulation scheme is described by:

x(t) = cos(omegac * t + phiDELTA * m (t))

where

omegac = 2 * pi * 103

phiDELTA = phi

m(t) = PI(t) = u(t + 1/2) - u(t - 1/2)

[2 pts.] a) Sketch x(t).

[8 pts.] b) Sketch Re{X(omega)}, noting maximum amplitudes, center frequencies, and frequency of first zero crossing.

Problem #2 (10 points)

A square wave x(t) is passed through an ideal diode. Sketch the spectrum at the output of the ideal diode Y(omega), labelling important frequencies and amplitudes. Recall for an ideal diode that vout = { 0, vin <

0 and vin, vin >= 0 }.

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EE 120, Midterm #2, Fall 1994

Sketch Y(omega).

Problem #3 (5 points)

The signal x(t) is passed through a lowpass filter with frequency response H(omega). The signal x(t) contains a sinusoidal component at 100 KHz. Sketch approximately y(t), the output in time of the lowpass filter for the input x(t).

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EE 120, Midterm #2, Fall 1994

Problem #4 (25 points)

You are given the following modulation scheme:

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EE 120, Midterm #2, Fall 1994

For each signal x1(t), x2(t), ..., x6(t), y(t) select one of the following sketches, specifying amplitude A0

and frequency omega1. (Hint: Amplitude A0 may be complex.)

letter of sketch A0 omega1

X1(omega)

X2(omega)

X3(omega)

X4(omega)

X5(omega)

X6(omega)

Y(omega)

The following sketches represent spectra of the signals x1(t) ... x6(t), and y(t). The horizontal and vertical

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EE 120, Midterm #2, Fall 1994

scale in each sketch are arbitrary, and should be considered independently.

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EE 120, Midterm #2, Fall 1994

Problem #5 (7 points)

A causal system is described by the following differential equation (with input x(t) and output y(t)) :

dy/dt = d2x/dt2 + 3 dx/dt + 2 x

Assuming zero initial conditions, a) Is this system BIBO stable? b) Find Y(s) and y(t) for x(t) = 0 and y(0-) = -5.

Problem #6 (3 points)

A system has Laplace Transform X(s) with ROC sigma < 2.

The system is (circle one) : a) stable but not causal b) causal but not stable c) stable and causal d) neither stable nor causal

Problem #7 (15 points)

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EE 120, Midterm #2, Fall 1994

a) With d(t) = 0, compute Y(s)/X(s). b) For which values of k1 and k2 is the system stable?

c) Let d(t) = u(t) and x(t) = 0, with k1 = 1 and k2 = 1. What is the limit of y(t) as t approaches infinity?

(answer should be a number) d) Let d(t) = 0 and x(t) = u(t), with k1 = 1 and k2 = 1. What is the limit of y(t) as t approaches infinity?

Problem #8 (25 points)

For each pole-zero diagram below, fill in the box with the letter of the corresponding frequency response and impulse response that follow. All diagrams represent causal systems.

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EE 120, Midterm #2, Fall 1994

Sketches to be used as answers for problem #8.

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EE 120, Midterm #2, Fall 1994

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EE 120, Midterm #2, Fall 1994

Solutions (page 1)Solutions (page 2)

Posted by HKN (Electrical Engineering and Computer Science Honor Society) University of California at Berkeley