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If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containing
- a)only sine terms
- b)only cosine terms
- c)cosine terms and constant terms
- d)sine terms and constant terms
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) c...
Explanation:
Dirichlet Conditions:
Dirichlet conditions are a set of criteria that a function must satisfy to be expanded in a Fourier series. These conditions are as follows:
1. The function must be single-valued and continuous in the interval for which it is being expanded.
2. The function must have a finite number of maxima and minima in the interval.
3. The function must have a finite number of discontinuities in the interval, which can be of the first kind (jump discontinuities) or the second kind (infinite discontinuities).
4. If the function has discontinuities, then the left and right limits of the function at the discontinuity point must exist and be finite.
f(t) = -f(-t):
The given function f(t) satisfies the odd symmetry property, i.e., f(t) = -f(-t). This means that the function is symmetric about the origin, and its Fourier series will only contain sine terms. This is because the Fourier series of an odd function only contains sine terms, while the Fourier series of an even function only contains cosine terms. Therefore, option A is the correct answer.
Conclusion:
In conclusion, if a function satisfies the odd symmetry property and the Dirichlet conditions, then its Fourier series will only contain sine terms.
Dirichlet Conditions:
Dirichlet conditions are a set of criteria that a function must satisfy to be expanded in a Fourier series. These conditions are as follows:
1. The function must be single-valued and continuous in the interval for which it is being expanded.
2. The function must have a finite number of maxima and minima in the interval.
3. The function must have a finite number of discontinuities in the interval, which can be of the first kind (jump discontinuities) or the second kind (infinite discontinuities).
4. If the function has discontinuities, then the left and right limits of the function at the discontinuity point must exist and be finite.
f(t) = -f(-t):
The given function f(t) satisfies the odd symmetry property, i.e., f(t) = -f(-t). This means that the function is symmetric about the origin, and its Fourier series will only contain sine terms. This is because the Fourier series of an odd function only contains sine terms, while the Fourier series of an even function only contains cosine terms. Therefore, option A is the correct answer.
Conclusion:
In conclusion, if a function satisfies the odd symmetry property and the Dirichlet conditions, then its Fourier series will only contain sine terms.
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If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) c...
Since negative sign is outside the function it will be an odd term and odd terms are sine functions
for dirichlet conditions constants are not required hence option a
for dirichlet conditions constants are not required hence option a
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If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer?.
If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If, f(t) = -f(-t)and f(t) satisfy the dirichlet conditions then f(t) can be expanded in a fourier series containinga)only sine termsb)only cosine termsc)cosine terms and constant termsd)sine terms and constant termsCorrect answer is option 'A'. Can you explain this answer?.
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