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Let δ(f) is the delta function the value of integral 
- a)1
- b)- 1
- c)0
- d)π/2
Correct answer is option 'A'. Can you explain this answer?
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Let δ(f) is the delta function the value of integrala)1b)- 1c)0d...
Understanding the Signal
The given periodic signal is:
v(t) = 30 sin(100t) + 10 cos(300t) + 6 sin(500t + π/4)
This signal is composed of three different frequency components.
Identifying Frequency Components
- The first term, 30 sin(100t), has an angular frequency of 100 rad/s.
- The second term, 10 cos(300t), has an angular frequency of 300 rad/s.
- The third term, 6 sin(500t + π/4), has an angular frequency of 500 rad/s.
Finding the Fundamental Frequency
To determine the fundamental frequency of a periodic signal, we need to find the greatest common divisor (GCD) of the angular frequencies of each component:
- 100 rad/s
- 300 rad/s
- 500 rad/s
Calculating GCD
- The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- The factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
- The factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The greatest common divisor among these is:
- GCD(100, 300, 500) = 100
Conclusion
Thus, the fundamental frequency of the signal v(t) is 100 rad/s, which corresponds to option 'A'. This frequency is the lowest frequency present in the signal and defines its periodicity.
The given periodic signal is:
v(t) = 30 sin(100t) + 10 cos(300t) + 6 sin(500t + π/4)
This signal is composed of three different frequency components.
Identifying Frequency Components
- The first term, 30 sin(100t), has an angular frequency of 100 rad/s.
- The second term, 10 cos(300t), has an angular frequency of 300 rad/s.
- The third term, 6 sin(500t + π/4), has an angular frequency of 500 rad/s.
Finding the Fundamental Frequency
To determine the fundamental frequency of a periodic signal, we need to find the greatest common divisor (GCD) of the angular frequencies of each component:
- 100 rad/s
- 300 rad/s
- 500 rad/s
Calculating GCD
- The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- The factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
- The factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The greatest common divisor among these is:
- GCD(100, 300, 500) = 100
Conclusion
Thus, the fundamental frequency of the signal v(t) is 100 rad/s, which corresponds to option 'A'. This frequency is the lowest frequency present in the signal and defines its periodicity.
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Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct 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 Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct 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 Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct answer is option 'A'. Can you explain this answer?.
Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct 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 Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct 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 Let δ(f) is the delta function the value of integrala)1b)- 1c)0d)π/2Correct answer is option 'A'. Can you explain this answer?.
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