GATE EC 2020 Set 1 — Question 62
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Signals & Systems → Continuous-Time Signals → Parseval's Theorem
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Question
is the Fourier transform of shown below. The value of (rounded off to two decimal places) is _______.
Correct answer
58.5 to 58.8
Solution
According to Parseval's theorem for the Fourier transform:From the given graph, is a piecewise linear function defined as:The energy of the signal is calculated by integrating the square of the function over its non-zero intervals:Evaluating each integral:
Now, applying Parseval's theorem:Rounding off to two decimal places, the value is 58.64.
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Total energy .Now, applying Parseval's theorem:Rounding off to two decimal places, the value is 58.64.
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