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If a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal to
- a)E
- b)E/2
- c)2E
- d)4E
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If a signal f(t) has energy ‘E’ the energy of the signal f...
Most Upvoted Answer
If a signal f(t) has energy ‘E’ the energy of the signal f...
Explanation:
Energy of a signal is given by the formula:
\[
E = \int_{-\infty}^{\infty} |f(t)|^2 dt
\]
Energy of f(2t):
When we have a signal f(t) and we consider f(2t), the energy of the signal f(2t) is given by:
\[
E' = \int_{-\infty}^{\infty} |f(2t)|^2 dt
\]
Change of variable:
Let's substitute a new variable \(\tau = 2t\), then \(dt = \frac{d\tau}{2}\).
\[
E' = \int_{-\infty}^{\infty} |f(\tau)|^2 \frac{d\tau}{2}
\]
\[
E' = \frac{1}{2} \int_{-\infty}^{\infty} |f(\tau)|^2 d\tau
\]
Comparison:
Comparing the expressions for \(E\) and \(E'\), we see that the energy of the signal f(2t) is half of the energy of the original signal f(t).
Therefore, the energy of the signal f(2t) is \(E/2\).
So, the correct answer is option B.
Energy of a signal is given by the formula:
\[
E = \int_{-\infty}^{\infty} |f(t)|^2 dt
\]
Energy of f(2t):
When we have a signal f(t) and we consider f(2t), the energy of the signal f(2t) is given by:
\[
E' = \int_{-\infty}^{\infty} |f(2t)|^2 dt
\]
Change of variable:
Let's substitute a new variable \(\tau = 2t\), then \(dt = \frac{d\tau}{2}\).
\[
E' = \int_{-\infty}^{\infty} |f(\tau)|^2 \frac{d\tau}{2}
\]
\[
E' = \frac{1}{2} \int_{-\infty}^{\infty} |f(\tau)|^2 d\tau
\]
Comparison:
Comparing the expressions for \(E\) and \(E'\), we see that the energy of the signal f(2t) is half of the energy of the original signal f(t).
Therefore, the energy of the signal f(2t) is \(E/2\).
So, the correct answer is option B.
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If a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal toa)Eb)E/2c)2Ed)4ECorrect answer is option 'B'. 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 a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal toa)Eb)E/2c)2Ed)4ECorrect answer is option 'B'. 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 a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal toa)Eb)E/2c)2Ed)4ECorrect answer is option 'B'. Can you explain this answer?.
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