University of Ha’il
College of Engineering, Department of Electrical Engineering
Signals Analysis EE207 - HW 1
Weighting: 100 Marks
Problem 1 (21 Marks):
Sketch each of the following signals as a function of the independent variable t
over the specified range if any:
(3 Marks Each)
1.
2.
3.
4.
5.
6.
7.
𝑿(𝟒 − 𝟒𝒕)
𝒖(𝟒 − 𝟒𝒕)
𝟐𝑿(−𝟑𝒕)
𝑿(𝒕 − )
𝑿( − 𝟒𝒕)
𝑿(𝒕 − 𝟒)
𝟑𝒕

𝑿(𝒕) = 𝐜𝐨𝐬( 𝟒 + 𝟖)
Problem 2 (18 Marks):
for
2 𝒕 −𝟏
Determine if the following signals are periodic. If yes, calculate the fundamental
period, frequency, and phase for the signals:
(3 Marks Each)
1.
2.
3.
4.
5.
x(t) =
x(t) =
x(t) =
x(t) =
x(t) =
2sin(4𝜋𝑡)
|2sin(4𝜋𝑡)|. Note: | . | is absolute value.
2sin( 4𝜋𝑡 + 6) + 2 cos( 20𝜋𝑡 + 6)
2sin( 4𝑡 + 6) + 2 cos( 20𝑡 + 6)

exp( 𝑗(5𝑡 + 4))
3
𝑡
6. x(t) = exp( 𝑗 ( 4 )) + exp(86)
Problem 3 (21 Marks):
Evaluate the following integrations:
(3 Marks Each)
4
1.
t
 e cos(t ) (t  2)dt
2
0
4
2.
e
t 2
cos(t ) (t  2)dt
0
∞
3𝜋𝑡
3. ∫−∞ [sin (
4
4.
− 1) 𝛿(𝑡 − 1)𝑑𝑡
5.
6.
7.
∞
∫−∞ sin(3𝑡
∞
∫−∞ sin(3𝑡
∞
∫−∞ sin(3𝑡
∞
∫−∞ sin(3𝑡
) + exp(−2𝑡 + 2)]𝛿(−𝑡 − 1)𝑑𝑡
− 1) 𝑢(𝑡 − 1)𝑑𝑡
− 1) 𝑟𝑒𝑐𝑡(𝑡 − 1)𝑑𝑡
− 1) 𝑢(𝑥 − 𝑡)𝑑𝑡
Problem 4 (20 Marks):
Prove the following:
(10 Marks Each)
∞
∫−∞ 𝑓(𝑡)𝛿(𝑡
∞
∫−∞ 𝛿(𝑡)𝑓(𝑡
− 𝑡0 )𝑑𝑡 = 𝑓(𝑡0 )
2.
− 𝑡0 )𝑑𝑡 = 𝑓(−𝑡0 )
Hint: use integration by parts and ∫ 𝛿(𝑡)𝑑𝑡 = 𝑢(𝑡)
1.
Problem 5 (20 Marks):
Solve the following problems in textbook
1.8, 1.9, 1.10, 1.11
HW 1
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