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EGGN 388 Fall 2006 Practice Exam #
All-or-none (5 points each)
- Which of the following expressions does not belong (circle one)?
a) 2
1
π ∠
b) j
c)
2
π j
e
d) none of the above
- The following expression is (circle one) TRUE or FALSE:
θ θ θ
j j e e
− 2 sin( )= +
- evaluates to be (circle one)
j ( 2 m )
e
π + π
a) - b) - j c) 0 d) m e) none of the above
- Give the correct complex magnitude for the sinusoidal signal (circle one):
() 20 cos( 2
π xt = π t +
a) 10 4
j^ π e
b) 20 4
j^ π e
−
c) 10 4
j^ π e
−
d) 20 4
j^ π e e) none of the above
- A sinusoidal signal with frequency 100 rad/sec has a complex magnitude 3 5
j^ π e
−
. What is the correct time-domain expression (circle one)?
a) cos(^2 (^3 )^100 ) 5
x ( t )= π t +
π
b) )^3 ) 5
x ( t )= 100 cos( 2 ( t +
π π
c) ) 5
() 3 cos( 2 ( 100 )
π xt = π t +
d) ) 5
() 3 cos( 2 ( 100 )
π xt = π t −
e) none of the above
- What is the distance (in seconds) between the peaks of the following two sinusoidal
signals:
) 6
() cos( 20
() cos( 20 )
2
1
π π
π
= −
=
x t t
x t t
Long Answer (show your work for partial credit – 10 points each)
- Write down an expression for x(t) from the following graph:
-3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
1
2
3
- Determine a formula for as a sum of cosines for a signal with the spectrum
shown.
x ( t )
- Match the waveforms on the next page to their spectrum.
Bonus: Show that
2 cos( ω 1 t )cos( ω 2 t )=cos(( ω 1 + ω 2 ) t )+cos(( ω 1 − ω 2 ) t )
