Exam (elaborations)
Exam (elaborations) Digital Signal Processing Digital Signal Processing Comprehensive Exams 1-8 Answered_ 2024.
Digital Signal Processing: Fundamentals and Applications, Third Edition [3rd Ed] Exam_ Answered.
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1Exam 1 (Chapter 1 to Chapter 3)
Show all your work for each problem.
1. Given the following DSP block diagram with a sampling rate of 4000 Hz, fill in each
blank block with the following given units.
fs=4000 Hz
ADC
coding DSP
DAC y (t )
y ( n)
a. Anti-image lowpass filter
b. Anti-aliasing lowpass filter
c. Sampler and hold circuit
d. Hold circuit
Answer the following questions:
e. Nyquist frequency =
f. Maximum frequency of the input analog signal that the DSP can handle
without aliasing
g. Identify the block that will cause signal distortion.
(10 points)
Answers: (b), (c), (d), (a)
e. 2000 Hz
f. 2000 Hz
g. (d)
, 2
2. Given the following labeled digital signals,
x ( n)
10.0
10
7.0711 7.0711
T 200
0.0 0.0 5 6 7
n (Discrete-time index)
1 0 1 2 3 4
5
7.0711 7.0711
10
10.0
t (Real time (micro-seconds))
0 T 2T 3T 4T 5T 6T 7T
Answer the following questions. (15 points)
a. Sampling period ______________________
b. Sampling rate ________________________
c. Nyquist limit ________________________
d. x(3) ______________________
e. If x(n) is the sampled version of the analog sine wave: x(t ) 10sin(t ) , what is the
frequency of the analog sine wave? ______________
Answers:
a. 200 s
b. 5000 Hz
c. 2500 Hz
d. x(3) 7.7011
e. 625 Hz
, 3
3. Sketch each of the following sequences for n 0,1, 2,3 .
a. x (n) 6 (n 1) 10 (n 3)
b. x (n) 6u(n 2)
bg
c. x (n) 0.8 u(n)
n
d. x(n) 10 sin(0.25n)u(n)
(20 points)
Answers:
(a) x(0) 0 , x(1) 6 , x(2) 0 , x(3) 10
(b) x(0) 0 , x(1) 0 , x(2) 6 , x(3) 6
(c) x(0) 1.0 , x(1) 0.8 , x(2) 0.64 , x(3) 0.512
(c) x(0) 0.0 , x(1) 7.071 , x(2) 10.0 , x(3) 7.071
10 6
5
4
(a)
(b)
0
2
-5
-10 0
0 1 2 3 4 5 0 1 2 3 4 5
Sample number n Sample number n
1 10
5
(c)
(d)
0.5 0
-5
0 -10
0 1 2 3 4 5 0 1 2 3 4 5
Sample number n Sample number n
, 4
4. Given a DSP system with a sampling rate f s 10000 Hz, that is, the sampling period
is T 100 us, and each input is shown below:
a. x(t ) 10cos(400 t )u(t ) , ________ f _________
b. v(t ) 10cos(17000 t )u (t ) , _______ f _________
(1) Plot spectrum for (a) and (b) for the range from -5000 Hz to 25000 Hz, respectively.
(2) Determine which one will be aliased. Explain.
(3) Using x(n) x(t ) t nT , determine the digital (DSP) sequences for x (n) (a) and v (n)
(b) respectively.
x ( n) _ _ _ _ _ _ _ _ _ _ _ _ _
v ( n) _ _ _ _ _ _ _ _ _ _ _ _ _
(20 points)
Answers:
(a) 400 radians/ second, f 200 Hz
(b) 17000 radians/second, f 8500 Hz
1)
(a)
Xs( f )
10 /T
f kHz
0.2 0.2 9.8 10 10.2 19.8 20 20.2
(b)
Vs ( f )
10 / T
f kHz
21.5 8.5 1.5 1.5 8.5 10 11.5 18.5 20 21.5
2) (b) is aliased. The sampling theory condition is not satisfied.
3) T 1/ f s 1/10000 0.0001 second
x(n) 10cos(0.04n )u (n)
v(n) 10cos(1.7n )u (n)
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