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The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is?
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The energy of the signal ,x(t) =e power -100 u(t) contained in the ban...
Calculation of Energy of the Signal x(t)
E = ∫(|X(f)|^2) df
E = ∫(1/(4π^2f^2 + 10^4)) df from 50π to ∞
E = 0.00044 Joules
Explanation
- The given signal is x(t) = e^(-100u(t))
- To calculate the energy of this signal, we need to find its Fourier Transform.
- The Fourier Transform of x(t) is X(f) = 1/(j2πf - 100), where j is the imaginary unit.
- The energy of the signal can be calculated using Parseval's Theorem:
E = ∫(|X(f)|^2) df
- Since the signal x(t) is causal, its Fourier Transform X(f) is zero for f < />
- Therefore, we need to integrate the square of the magnitude of X(f) over the range f > 50π Hz.
- Substituting X(f) in the above equation, we get:
E = ∫(1/(4π^2f^2 + 10^4)) df from 50π to ∞
- Integrating this expression gives the energy of the signal in the frequency range f > 50π Hz.
- After performing the integration, we get:
E = 0.00044 Joules
Explanation
- The given signal x(t) is a decaying exponential function with a time constant of 1/100 seconds.
- The Fourier Transform of the signal is a Lorentzian function centered at 100 Hz.
- The energy of the signal in the frequency range f > 50π Hz can be calculated by integrating the square of the magnitude of its Fourier Transform over this frequency range.
- Parseval's Theorem relates the energy of a signal to the square of its Fourier Transform.
- By substituting the Fourier Transform of the signal in the Parseval's Theorem, we can calculate the energy of the signal in the frequency range f > 50π Hz.
- The energy of the signal is a measure of the total power contained in the signal over this frequency range.
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The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is?
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The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is? 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 The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is?.
The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is? 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 The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The energy of the signal ,x(t) =e power -100 u(t) contained in the band mode f > then equal to 50 pi hz is?.
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