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Please solve all the questions in the pdf document “Assgt02”. you can solve it on paper and then scan it. please use the “useful tables” attached to help you solve the assignment.EECE426–Communication Systems II
Table 1: Fourier Transform Pairs.
Tables: Page 1 / 4
EECE426–Communication Systems II
Table 2: Properties of Fourier Transform.
Some Useful Mathematical Relationships
cos( x) =
e jx + e – jx
2
e jx – e – jx
sin( x) =
2 j Relationships.
Table 3: Useful Trigonometric
cos( x ± y ) = cos( x) cos( y ) m sin( x) sin( y )
sin( x ± y ) = sin( x) cos( y ) ± cos( x) sin( y )
cos(2 x) = cos 2 ( x) – sin 2 ( x)
sin( 2 x) = 2 sin( x) cos( x)
2 cos2 ( x) = 1 + cos(2 x)
2 sin 2 ( x) = 1 – cos(2 x)
cos 2 ( x) + sin 2 ( x) = 1
2 cos( x) cos( y ) = cos( x – y ) + cos( x + y )
2 sin( x) sin( y ) = cos( x – y ) – cos( x + y )
2 sin( x) cos( y ) = sin( x – y ) + sin( x + y )
Tables: Page 2 / 4
EECE426–Communication Systems II
Useful Integrals
Table 4: Useful Integrals.
ò cos( x)dx
sin(x)
ò sin( x)dx
– cos(x)
ò x cos( x)dx
cos( x) + x sin( x)
ò x sin( x)dx
sin( x) – x cos( x)
òx
2
cos( x)dx
2 x cos( x) + ( x 2 – 2) sin( x)
òx
2
sin( x)dx
2 x sin( x) – ( x 2 – 2) cos( x)
ax
dx
e ax
a
òe
ò xe
òx
ax
dx
2 ax
e dx
dx
ò a + bx
dx
ò a 2 + b 2×2
éx 1 ù
e ax ê – 2 ú
ëa a û
é x 2 2x 2 ù
e ê – 2 – 3ú
a û
ëa a
ax
1
ln a + bx
b
bx
1
tan -1 ( )
ab
a
Tables: Page 3 / 4
EECE426–Communication Systems II
E&CE 411, Spring 2009, Table of Q Function
1
Table 5: Q-Function.
x
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
Q(x)
0.5
0.48006
0.46017
0.44038
0.42074
0.40129
0.38209
0.36317
0.34458
0.32636
0.30854
0.29116
0.27425
0.25785
0.24196
0.22663
0.21186
0.19766
0.18406
0.17106
0.15866
0.14686
0.13567
0.12507
0.11507
0.10565
0.0968
0.088508
0.080757
0.073529
0.066807
0.060571
0.054799
0.049471
0.044565
0.040059
0.03593
0.032157
0.028717
0.025588
0.02275
0.020182
0.017864
0.015778
0.013903
0.012224
x
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
Table 1: Values
Q(x)
0.010724
0.0093867
0.0081975
0.0071428
0.0062097
0.0053861
0.0046612
0.0040246
0.003467
0.0029798
0.0025551
0.002186
0.0018658
0.0015889
0.0013499
0.0011442
0.0009676
0.00081635
0.00068714
0.00057703
0.00048342
0.00040406
0.00033693
0.00028029
0.00023263
0.00019262
0.00015911
0.00013112
0.0001078
8.8417×10−5
7.2348×10−5
5.9059×10−5
4.8096×10−5
3.9076×10−5
3.1671×10−5
2.5609×10−5
2.0658×10−5
1.6624×10−5
1.3346×10−5
1.0689×10−5
8.5399×10−6
6.8069×10−6
5.4125×10−6
4.2935×10−6
3.3977×10−6
of Q(x) for 0 ≤ x ≤ 9
x
Q(x)
4.55 2.6823×10−6
4.60 2.1125×10−6
4.65 1.6597×10−6
4.70 1.3008×10−6
4.75 1.0171×10−6
4.80 7.9333×10−7
4.85 6.1731×10−7
4.90 4.7918×10−7
4.95 3.7107×10−7
5.00 2.8665×10−7
5.05 2.2091×10−7
5.10 1.6983×10−7
5.15 1.3024×10−7
5.20 9.9644×10−8
5.25
7.605×10−8
5.30 5.7901×10−8
5.35 4.3977×10−8
5.40
3.332×10−8
5.45 2.5185×10−8
5.50
1.899×10−8
5.55 1.4283×10−8
5.60 1.0718×10−8
5.65 8.0224×10−9
5.70 5.9904×10−9
5.75 4.4622×10−9
5.80 3.3157×10−9
5.85 2.4579×10−9
5.90 1.8175×10−9
5.95 1.3407×10−9
6.00 9.8659×10−10
6.05 7.2423×10−10
6.10 5.3034×10−10
6.15 3.8741×10−10
6.20 2.8232×10−10
6.25 2.0523×10−10
6.30 1.4882×10−10
6.35 1.0766×10−10
6.40 7.7688×10−11
6.45 5.5925×10−11
6.50 4.016×10−11
6.55 2.8769×10−11
6.60 2.0558×10−11
6.65 1.4655×10−11
6.70 1.0421×10−11
6.75 7.3923×10−12
x
6.80
6.85
6.90
6.95
7.00
7.05
7.10
7.15
7.20
7.25
7.30
7.35
7.40
7.45
7.50
7.55
7.60
7.65
7.70
7.75
7.80
7.85
7.90
7.95
8.00
8.05
8.10
8.15
8.20
8.25
8.30
8.35
8.40
8.45
8.50
8.55
8.60
8.65
8.70
8.75
8.80
8.85
8.90
8.95
9.00
Q(x)
5.231×10−12
3.6925×10−12
2.6001×10−12
1.8264×10−12
1.2798×10−12
8.9459×10−13
6.2378×10−13
4.3389×10−13
3.0106×10−13
2.0839×10−13
1.4388×10−13
9.9103×10−14
6.8092×10−14
4.667×10−14
3.1909×10−14
2.1763×10−14
1.4807×10−14
1.0049×10−14
6.8033×10−15
4.5946×10−15
3.0954×10−15
2.0802×10−15
1.3945×10−15
9.3256×10−16
6.221×10−16
4.1397×10−16
2.748×10−16
1.8196×10−16
1.2019×10−16
7.9197×10−17
5.2056×10−17
3.4131×10−17
2.2324×10−17
1.4565×10−17
9.4795×10−18
6.1544×10−18
3.9858×10−18
2.575×10−18
1.6594×10−18
1.0668×10−18
6.8408×10−19
4.376×10−19
2.7923×10−19
1.7774×10−19
1.1286×10−19
Tables: Page 4 / 4
Assignment2 – EECE326
School of Engineering
American University in Dubai
Course: EECE326–Communication Systems I w/Lab
Semester: Spring 2021
Instructor: Dr. Khaled Ali
Due Date: 14 Feb, 2021 @ 2:00 pm
Name:
ID:
Signature:
Major:
Submission Guidelines:
• Your submission should be emailed to kali@aud.edu, by 14 Feb, 2021 @ 2:00 pm.
– your email should be titled: Assignment2 EECE326 Spring 2021
• Save your file as follows:
Assignment2-EECE326-Sec#-FirstName-LastName.pdf
– if you are submitting more than one file (eg: MATLAB file and pdf file), combine
all your files in a single “.zip” file and save it according to the aforementioned
naming conventions.
• Marks will be deducted for lack of neatness or organization.
– Discussion based questions should be typed.
– Problem-solving based questions can be hand-written. However, illegible submissions or submissions with scratches will result in deduction of marks.
– Number each page and write your name on it.
• Solve this assignment on your own.
• Solve all questions to avoid receiving a zero, if only selected questions are marked.
• Failure to abide with submission guidelines will result in deduction of marks.
• Late submissions will not be accepted.
* By signing above you confirm that the submission has been fully prepared by you. Any suspicion of copying or plagiarism in this work will be reported to the Dean or Chair for appropriate
investigation and appropriate disciplinary actions, which may result in a “0” on the work, an “F”
in the course or other penalties as described in the Student Handbook, which can be found online
at: http://www.aud.edu/files/StudentHandbook.pdf
Page 1 of 2
EECE326–Communication Systems I w/Lab
Spring 2021
1. Using the Fourier transform tables (pairs and/or properties), determine the following:
(a) Auto-correlation of x(t) = e−2t u(t).
(b) The received signal y(t), if the signal x(t) = 5sinc2 (5πt) is transmitted through the LTI
channel h(t) = 10sinc(10πt).
(c) R(f ) and P (f ) in terms G(f ), where R(f ), P (f ), and G(f ) are the Fourier transforms
of the signals g(t) =, r(t), and p(t), respectively, which are shown in Fig. 1.
g(t)
1
0.5
-3
-2
-1
1
2
3
1
2
3
1
2
3
r(t)
1
0.5
-3
-2
-1
p(t)
1
0.5
-3
-2
-1
Figure 1: Signals for Question 1c
2. Consider the signals m(t) = 2 sin(2πt), c(t) = cos(2π20t), and x(t) = m(t)c(t) .
(a)
(b)
(c)
(d)
Sketch the Fourier transform of m(t).
Sketch the Fourier transform of x(t)
Determine the bandwidth of all three signals?
Determine the power of all three signals?
3. Consider the LTI channel h(t) = 2sinc(πt) sin(πt).
(a) Sketch the magnitude and phase frequency responses of the channel.
(b) Determine the bandwidth of the channel.
(c) If a signal with bandwidth less than the bandwidth of h(t) is transmitted through h(t),
will this result in distortionless transmission? Why or why not?
Assignment2: Page 2 / 2

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