[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate and coded using a PCM system having a 128 levels quantizer. The binary data is sent through a 2.5km transmission channel after been modulated as MPSK. The bandwidth of this channel is set to be 78% of the operating binary rate. Assume the power spectral density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of the received signal (in dB) to ensure the operating BER is not worse than 78 error bits per second. (Use TB21.9). a ob (1+²1²
[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate and coded using a PCM system having a 128 levels quantizer. The binary data is sent through a 2.5km transmission channel after been modulated as MPSK. The bandwidth of this channel is set to be 78% of the operating binary rate. Assume the power spectral density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of the received signal (in dB) to ensure the operating BER is not worse than 78 error bits per second. (Use TB21.9). a ob (1+²1²
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Concept explainers
Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
Probability of Error
This topic is widely taught in many undergraduate and postgraduate degree courses of:
Question
![[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate
and coded using a PCM system having a 128 levels quantizer. The binary data is sent
through a 2.5km transmission channel after been modulated as MPSK. The bandwidth
of this channel is set to be 78% of the operating binary rate. Assume the power spectral
density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of
the received signal (in dB) to ensure the operating BER is not worse than 78 error bits
per second. (Use ToB≥ 1.9).
(1+5
The above question is similar to
this question, but with the
numbers changing, solve the
question in the same way and steps
(12) A baseband signal (band-limited to 4.5kHz) is sampled at 22% over Nyquist rate
and coded using PCM system having 256 levels quantizer. The resulting NRZ
unipolar binary data is planned to be sent through a 2km transmission channel
after been modulated with M-ary PSK. The bandwidth of this channel was set
to be 78% of the operating binary rate. If the channel is contaminated by a
Gaussian zero-mean white noise of PSD = 2.5nW/Hz per km, calculate the
required minimum r.m.s. power of the received signal (in dBm) to ensure the
operating BER is not worse than 120 error bits per second. (Use TB≥ 1.7).
Solution: R = lfs = 8 x 2.44 x 4.5 x 10³ = 87.84 kbps,
=
m
Bch = 0.78R = 68.5152kHz. To Bch = 1.7 Rg = 40.3031k symbols per
second, m =
Rb
R=2.17953 bits per symbol. → Rs = 29.28 k symbols
per second. P, =BER = 1.3661 x 10-3. n = 2 x 2.5 = 5nW/Hz.
→Q¹(2.0492 x 10-3) = 44.7285√S
>
25
mP = 2Q (√√x sin)
nRs
X
S = (287)² = 4.1171mW: S≥6.1459dBm
44.7285
The Q function can be approximated as:
Q(x) e(az²+bx+c)
For 0 ≤ x ≤ 8, the variables are: a = -0.4698, b=-0.5026, c= -0.8444.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df24b46-1f35-45c2-9a6b-667b76c49399%2F67d17eea-a9d0-478c-ab4b-d33271098a4e%2F1lwq84h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate
and coded using a PCM system having a 128 levels quantizer. The binary data is sent
through a 2.5km transmission channel after been modulated as MPSK. The bandwidth
of this channel is set to be 78% of the operating binary rate. Assume the power spectral
density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of
the received signal (in dB) to ensure the operating BER is not worse than 78 error bits
per second. (Use ToB≥ 1.9).
(1+5
The above question is similar to
this question, but with the
numbers changing, solve the
question in the same way and steps
(12) A baseband signal (band-limited to 4.5kHz) is sampled at 22% over Nyquist rate
and coded using PCM system having 256 levels quantizer. The resulting NRZ
unipolar binary data is planned to be sent through a 2km transmission channel
after been modulated with M-ary PSK. The bandwidth of this channel was set
to be 78% of the operating binary rate. If the channel is contaminated by a
Gaussian zero-mean white noise of PSD = 2.5nW/Hz per km, calculate the
required minimum r.m.s. power of the received signal (in dBm) to ensure the
operating BER is not worse than 120 error bits per second. (Use TB≥ 1.7).
Solution: R = lfs = 8 x 2.44 x 4.5 x 10³ = 87.84 kbps,
=
m
Bch = 0.78R = 68.5152kHz. To Bch = 1.7 Rg = 40.3031k symbols per
second, m =
Rb
R=2.17953 bits per symbol. → Rs = 29.28 k symbols
per second. P, =BER = 1.3661 x 10-3. n = 2 x 2.5 = 5nW/Hz.
→Q¹(2.0492 x 10-3) = 44.7285√S
>
25
mP = 2Q (√√x sin)
nRs
X
S = (287)² = 4.1171mW: S≥6.1459dBm
44.7285
The Q function can be approximated as:
Q(x) e(az²+bx+c)
For 0 ≤ x ≤ 8, the variables are: a = -0.4698, b=-0.5026, c= -0.8444.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,