I have a question about the parseval relation written here https://en.wikipedia.org/wiki/Parseval%27s_theorem (In the chapter Notation used in physics).
If I have a signal continuous but limited (so it does not go from $\infty$ to $\infty$ but from 0 to T, can The Parseval theorem be applied?
Answer
Sure. You can can just integrate in the time domain from $0$ to $T$ since the area outside $[0, T]$ is 0.
Please note that you still must integrate from $-\infty$ to $+\infty$ in the frequency domain since finite support in the time domain implies infinite support in the frequency domain (and vice versa).
Things are different if the function is periodic.
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