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(ELEC211)01fallfinalsol.pdf
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ELEC 211 Final Examination 18 December 2001
Remarks: (1) Do all six problems. (2) The 1st problem has 15 points, and the 2nd C 6th problems have 6, 8, 6, 8, and 12 points, respectively.
1. Select the correct answer for each of the following question (choose one answer only and write down the answer on the provided answer book).
1-1. An LTI system (continuous-time or discrete-time) possesses the following properties:
(a)
linear and stable

(b)
time-invariant and stable

(c)
linear or time-invariant

(d)
linear and time-invariant


1-2. Which of the following is definitely not true for the energy and power of a signal computed over the whole time axis:
(a)
its energy and power are both finite

(b)
its energy and power are both infinite

(c)
its power is finite and its energy is infinite

(d)
its energy is finite and its power is zero


1-3. Which of the followings is definitely not true for the sinusoidal signal x(t) = 2 cos(w0t)?
(a)
it is a periodic signal

(b)
it has a Fourier transform consisting of two impulses

(c)
it is an eigen-signal to any continuous-time LTI systems

(d)
it is a real signal


1-4. Compared to x(t) , the new signal x(at) where 0 < a< 1 has been
(a)
expanded in the time-domain as well as in the frequency-domain

(b)
expanded in the time-domain but shrunk in the frequency-domain

(c)
shrunk in the time-domain as well as in the frequency-domain

(d)
shrunk in the time-domain but expanded in the frequency-domain


1-5. Which of the following interconnections of two stable systems might result in an un-stable system
(a)
cascade of these two systems

(b)
parallel of these two systems

(c)
feedback of these two systems

(d)
none of the above


1-6. Which of the following properties is not true for the convolution (both integral and sum):
(a)
distributivity (over addition)

(b)
distributivity (over multiplication)

(c)
associativity

(d)
commutativity


1-7. Which of the following parts is not included in the Dirichlet conditions for a periodic signal x(t) to have the Fourier series representation
(a)
x(t) is continuous everywhere

(b)
x(t) is absolutely integrable over one period

(c)
there exists at most a finite number of maxima and minima in x(t) over any finite interval of time

(d)
there exists at most a finite number of discontinuities in x(t) over any finite interval of time


1-8. The Fourier transform of a real, odd signal (continuous-time) is
(a) a constant (b) real-valued (c) purely imaginary and even (d) purely imaginary and odd
1-9. Which of the following for a discrete-time signal x[n] is not a continuous function
(a) its (discrete-time) Fourier transform (b) its z-transform (c) its unilateral z-transform (d) none of the above

1-10. A filter is said to have linear phase if
(a)
its coefficients are all real-valued

(