Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > A signal has a bandwidth of 1 MHz. It is samp...
Start Learning for Free
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.
Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would be
- a)60.4 dB
- b)70.3 dB
- c)50.1 dB
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher ...
Nyquist Rate = 2 MHz
This question is part of UPSC exam. View all Electronics and Communication Engineering (ECE) courses
Most Upvoted Answer
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher ...
Given Information
- Bandwidth of the signal = 1 MHz
- Sampling rate = 50% higher than Nyquist rate
- Quantization level = 256
- Quantizer step size = 225
- Sampling rate should be 20% above the Nyquist rate
To find
- Maximum SNR that can be realized without increasing the transmission bandwidth
Solution
Nyquist Rate:
The Nyquist rate is defined as the minimum sampling rate required to reconstruct a signal without any loss of information. It is given by the formula:
Nyquist rate = 2 x Bandwidth
Nyquist rate = 2 x 1 MHz = 2 MHz
Sampling Rate:
The given sampling rate is 50% higher than the Nyquist rate. Therefore, the sampling rate is:
Sampling rate = 1.5 x 2 MHz = 3 MHz
Quantization:
The given quantization level is 256, which means that the quantizer step size is:
Quantizer step size = (maximum signal amplitude) / (number of quantization levels - 1)
Quantizer step size = (2 x maximum signal amplitude) / 255
Quantizer step size = 225
From the above two equations, we get:
Maximum signal amplitude = (255 x Quantizer step size) / 2
Maximum signal amplitude = (255 x 225) / 2
Maximum signal amplitude = 28687.5
Sampling Rate for Maximum SNR:
The sampling rate should be 20% above the Nyquist rate. Therefore, the sampling rate for maximum SNR is:
Sampling rate = 1.2 x 2 MHz = 2.4 MHz
Signal-to-Quantization-Noise Ratio (SQNR):
The SQNR is given by the formula:
SQNR = (6.02 x number of bits) + 1.76 dB
SQNR = (6.02 x log2(number of quantization levels)) + 1.76 dB
SQNR = (6.02 x log2(256)) + 1.76 dB
SQNR = 49.92 dB
Noise Power:
The quantization noise power is given by the formula:
Noise power = (quantizer step size)² / 12
Noise power = (225)² / 12
Noise power = 4218.75
Signal Power:
The maximum signal amplitude is 28687.5. Therefore, the signal power is:
Signal power = (maximum signal amplitude)² / 2
Signal power = (28687.5)² / 2
Signal power = 412,748,046.875
SNR:
The SNR is given by the formula:
SNR = Signal power / Noise power
SNR = 412,748,046.875 / 4218.75
SNR = 97,856.96
Actual Sampling Rate:
The actual sampling rate is 3 MHz, which is greater than the required sampling rate of 2.4 MHz. Therefore, the SNR will be reduced due to aliasing. The aliasing noise is given by the formula:
Aliasing noise power = (sampling rate - required sampling rate) / sampling rate x Signal power
Aliasing noise power = (3 MHz - 2.4 MHz) / 3 MHz x 412,748,046.875
Aliasing noise power = 37,025
- Bandwidth of the signal = 1 MHz
- Sampling rate = 50% higher than Nyquist rate
- Quantization level = 256
- Quantizer step size = 225
- Sampling rate should be 20% above the Nyquist rate
To find
- Maximum SNR that can be realized without increasing the transmission bandwidth
Solution
Nyquist Rate:
The Nyquist rate is defined as the minimum sampling rate required to reconstruct a signal without any loss of information. It is given by the formula:
Nyquist rate = 2 x Bandwidth
Nyquist rate = 2 x 1 MHz = 2 MHz
Sampling Rate:
The given sampling rate is 50% higher than the Nyquist rate. Therefore, the sampling rate is:
Sampling rate = 1.5 x 2 MHz = 3 MHz
Quantization:
The given quantization level is 256, which means that the quantizer step size is:
Quantizer step size = (maximum signal amplitude) / (number of quantization levels - 1)
Quantizer step size = (2 x maximum signal amplitude) / 255
Quantizer step size = 225
From the above two equations, we get:
Maximum signal amplitude = (255 x Quantizer step size) / 2
Maximum signal amplitude = (255 x 225) / 2
Maximum signal amplitude = 28687.5
Sampling Rate for Maximum SNR:
The sampling rate should be 20% above the Nyquist rate. Therefore, the sampling rate for maximum SNR is:
Sampling rate = 1.2 x 2 MHz = 2.4 MHz
Signal-to-Quantization-Noise Ratio (SQNR):
The SQNR is given by the formula:
SQNR = (6.02 x number of bits) + 1.76 dB
SQNR = (6.02 x log2(number of quantization levels)) + 1.76 dB
SQNR = (6.02 x log2(256)) + 1.76 dB
SQNR = 49.92 dB
Noise Power:
The quantization noise power is given by the formula:
Noise power = (quantizer step size)² / 12
Noise power = (225)² / 12
Noise power = 4218.75
Signal Power:
The maximum signal amplitude is 28687.5. Therefore, the signal power is:
Signal power = (maximum signal amplitude)² / 2
Signal power = (28687.5)² / 2
Signal power = 412,748,046.875
SNR:
The SNR is given by the formula:
SNR = Signal power / Noise power
SNR = 412,748,046.875 / 4218.75
SNR = 97,856.96
Actual Sampling Rate:
The actual sampling rate is 3 MHz, which is greater than the required sampling rate of 2.4 MHz. Therefore, the SNR will be reduced due to aliasing. The aliasing noise is given by the formula:
Aliasing noise power = (sampling rate - required sampling rate) / sampling rate x Signal power
Aliasing noise power = (3 MHz - 2.4 MHz) / 3 MHz x 412,748,046.875
Aliasing noise power = 37,025
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
Question Description
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: It was found that a sampling rate 20% above therate would be adequate. So the maximum SNR, thatcan be realized without increasing the transmission bandwidth, would bea)60.4 dBb)70.3 dBc)50.1 dBd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
x
![]()
For Your Perfect Score in Electronics and Communication Engineering (ECE)
The Best you need at One Place
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup