Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > The trigonometric Fourier series expansion of... Start Learning for Free
The trigonometric Fourier series expansion of an odd function shall have
- a)only sine terms
- b)only cosine terms
- c)odd harmonics of both sine and cosine terms
- d)none of the these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The trigonometric Fourier series expansion of an odd function shall ha...
Understanding the Fourier Series of Odd Functions
When considering the Fourier series expansion of functions, it's important to understand how different types of functions (even, odd) affect the series representation.
Odd Functions
- An odd function is defined by the property f(-x) = -f(x).
- This symmetry implies that the function is symmetric about the origin.
Fourier Series Components
The Fourier series expansion of a periodic function can be expressed as:
- f(x) = a0/2 + Σ [an * cos(nωx) + bn * sin(nωx)]
Where:
- a0 is the average value of the function.
- an are the coefficients for the cosine terms (even functions).
- bn are the coefficients for the sine terms (odd functions).
Why Only Sine Terms for Odd Functions?
- For odd functions, the average value (a0) is zero because the positive and negative areas cancel each other out over one period.
- The cosine terms (an) are eliminated because they represent even functions, which do not satisfy the symmetry of odd functions.
- Thus, only sine terms (bn) remain, representing the odd harmonics of the function.
Conclusion
In conclusion, when performing a Fourier series expansion for an odd function, the result will contain only sine terms. Therefore, the correct answer is:
- a) only sine terms.
When considering the Fourier series expansion of functions, it's important to understand how different types of functions (even, odd) affect the series representation.
Odd Functions
- An odd function is defined by the property f(-x) = -f(x).
- This symmetry implies that the function is symmetric about the origin.
Fourier Series Components
The Fourier series expansion of a periodic function can be expressed as:
- f(x) = a0/2 + Σ [an * cos(nωx) + bn * sin(nωx)]
Where:
- a0 is the average value of the function.
- an are the coefficients for the cosine terms (even functions).
- bn are the coefficients for the sine terms (odd functions).
Why Only Sine Terms for Odd Functions?
- For odd functions, the average value (a0) is zero because the positive and negative areas cancel each other out over one period.
- The cosine terms (an) are eliminated because they represent even functions, which do not satisfy the symmetry of odd functions.
- Thus, only sine terms (bn) remain, representing the odd harmonics of the function.
Conclusion
In conclusion, when performing a Fourier series expansion for an odd function, the result will contain only sine terms. Therefore, the correct answer is:
- a) only sine terms.
 | Explore Courses for Electronics and Communication Engineering (ECE) exam |  |
Top Courses for Electronics and Communication Engineering (ECE)View all
Top Courses for Electronics and Communication Engineering (ECE)
Question Description
The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 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 The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer?.
The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 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 The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. 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 The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The trigonometric Fourier series expansion of an odd function shall havea)only sine termsb)only cosine termsc)odd harmonics of both sine and cosine termsd)none of the theseCorrect answer is option 'A'. 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 | |
Top Courses for Electronics and Communication Engineering (ECE)
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
