Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > . Every fourfold increase in the size N of th...
Start Learning for Free
. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.
- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
. Every fourfold increase in the size N of the DFT requires an additio...
Explanation: We know that, the variance of the quantization errors is directly proportional to the size N of the DFT. So, every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.
Most Upvoted Answer
. Every fourfold increase in the size N of the DFT requires an additio...
Understanding the DFT and Quantization Errors
The Discrete Fourier Transform (DFT) is a mathematical technique used in signal processing to analyze the frequency components of discrete signals. As the size \( N \) of the DFT increases, the precision required in computations also increases.
The Relationship Between DFT Size and Computational Precision
- When the size of the DFT quadruples (i.e., a fourfold increase), you are essentially processing a larger amount of data.
- This increase in data size leads to more detailed frequency resolution, but it also amplifies the quantization errors that can occur during signal representation and processing.
Quantization Errors Explained
- Quantization errors arise when continuous signals are converted to discrete values, introducing small inaccuracies.
- As \( N \) increases, the number of discrete levels available for quantization grows, which means that the representation of the signal becomes finer. However, it also means the errors can become more pronounced.
Why One Additional Bit is Necessary
- Each additional bit in computational precision effectively doubles the number of discrete levels available, thus reducing quantization error.
- To maintain the same level of accuracy in the face of increased data size and complexity, one extra bit of precision is required for every fourfold increase in \( N \). This ensures that the quantization errors do not propagate unbounded, preserving the fidelity of the signal processing.
Conclusion
- Thus, the statement is true: every fourfold increase in the size \( N \) of the DFT indeed requires an additional bit in computational precision to offset the additional quantization errors.
The Discrete Fourier Transform (DFT) is a mathematical technique used in signal processing to analyze the frequency components of discrete signals. As the size \( N \) of the DFT increases, the precision required in computations also increases.
The Relationship Between DFT Size and Computational Precision
- When the size of the DFT quadruples (i.e., a fourfold increase), you are essentially processing a larger amount of data.
- This increase in data size leads to more detailed frequency resolution, but it also amplifies the quantization errors that can occur during signal representation and processing.
Quantization Errors Explained
- Quantization errors arise when continuous signals are converted to discrete values, introducing small inaccuracies.
- As \( N \) increases, the number of discrete levels available for quantization grows, which means that the representation of the signal becomes finer. However, it also means the errors can become more pronounced.
Why One Additional Bit is Necessary
- Each additional bit in computational precision effectively doubles the number of discrete levels available, thus reducing quantization error.
- To maintain the same level of accuracy in the face of increased data size and complexity, one extra bit of precision is required for every fourfold increase in \( N \). This ensures that the quantization errors do not propagate unbounded, preserving the fidelity of the signal processing.
Conclusion
- Thus, the statement is true: every fourfold increase in the size \( N \) of the DFT indeed requires an additional bit in computational precision to offset the additional quantization errors.
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
Question Description
. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?.
. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice . Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) 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.
|
© 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