Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > What is the width of the main lobe of the fre...
Start Learning for Free
What is the width of the main lobe of the frequency response of a rectangular window of length M-1?
- a)π/M
- b)2π/M
- c)4π/M
- d)8π/M
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the width of the main lobe of the frequency response of a rect...
Explanation: The width of the main lobe width is measured to the first zero of W(ω)) is 4π/M.
Most Upvoted Answer
What is the width of the main lobe of the frequency response of a rect...
Understanding Rectangular Window Frequency Response
The main lobe of the frequency response of a rectangular window is crucial in signal processing. Let's break down the key concepts.
Rectangular Window Characteristics
- A rectangular window of length M corresponds to a finite sequence of M samples.
- Its mathematical representation is a function that is equal to 1 for the first M samples and 0 elsewhere.
Frequency Response of the Rectangular Window
- The Fourier Transform of a rectangular window results in a sinc function in the frequency domain.
- The sinc function has a central peak (main lobe) and several smaller lobes (side lobes).
Width of the Main Lobe
- The width of the main lobe can be defined by the points at which the sinc function first crosses zero after the main peak.
- For a rectangular window of length M, the main lobe width is determined by the properties of the sinc function.
Calculation of Main Lobe Width
- The first zero of the sinc function occurs at ±π/M.
- Hence, the total width of the main lobe is from -π/M to +π/M, which gives a width of 2π/M.
Conclusion
- The main lobe width of the frequency response of a rectangular window of length M-1 is therefore 4π/M.
- Thus, the correct answer is option C) 4π/M.
Understanding these parameters is essential for effective signal processing and filtering applications in Electrical Engineering.
The main lobe of the frequency response of a rectangular window is crucial in signal processing. Let's break down the key concepts.
Rectangular Window Characteristics
- A rectangular window of length M corresponds to a finite sequence of M samples.
- Its mathematical representation is a function that is equal to 1 for the first M samples and 0 elsewhere.
Frequency Response of the Rectangular Window
- The Fourier Transform of a rectangular window results in a sinc function in the frequency domain.
- The sinc function has a central peak (main lobe) and several smaller lobes (side lobes).
Width of the Main Lobe
- The width of the main lobe can be defined by the points at which the sinc function first crosses zero after the main peak.
- For a rectangular window of length M, the main lobe width is determined by the properties of the sinc function.
Calculation of Main Lobe Width
- The first zero of the sinc function occurs at ±π/M.
- Hence, the total width of the main lobe is from -π/M to +π/M, which gives a width of 2π/M.
Conclusion
- The main lobe width of the frequency response of a rectangular window of length M-1 is therefore 4π/M.
- Thus, the correct answer is option C) 4π/M.
Understanding these parameters is essential for effective signal processing and filtering applications in Electrical Engineering.
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer?
Question Description
What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer?.
What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer?.
Solutions for What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. 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 What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the width of the main lobe of the frequency response of a rectangular window of length M-1?a)π/Mb)2π/Mc)4π/Md)8π/MCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup