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some days ago I asked here parseval for a continuos but limited signal if the Parseval can be applied for limited signal.

Can you recommend me a book or a paper that I can use as reference for this?

Can someone show me the demonstration considering a limited domain

Thank you

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    $\begingroup$ The result follows trivially from the definition; I doubt there are any books that devote space to this. Can you clarify what you're trying to do, and why do you need this reference? $\endgroup$
    – MBaz
    Jul 15, 2019 at 22:21
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    $\begingroup$ @MBaz I have to justify it on a report. My advisor critised the fact that I used in the integral of the time signal a limit fro 0 to T, and asked me for references. $\endgroup$ Jul 16, 2019 at 7:50
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    $\begingroup$ @LucaMirtanini what did you write in your report, exactly? $\endgroup$
    – AlexTP
    Jul 16, 2019 at 11:31
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    $\begingroup$ @AlexTP I have simply written : $\int_{t0}^{t0+T} |x(t)|^2dt= \int_{-\infty}^{\infty}|X(f)|^2df$ . I don't think I did something wrong $\endgroup$ Jul 16, 2019 at 12:02

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I don't think you will find a reference for this. Your are simply stating that "integrating over a whole bunch of zeros results in 0". In other words, if $$x(t) = 0, x\not\in [0,T]$$ then $$ \int_{-\infty}^{+\infty}x(t) dt = \int_{-\infty}^{0}x(t) dt + \int_{0}^{T}x(t) dt + \int_{T}^{+\infty}x(t)dt = \int_{0}^{T}x(t) dt $$ since $$ \int_{-\infty}^{0}x(t) dt = \int_{-\infty}^{0}0 dt=0$$ and

$$\int_{T}^{+\infty}x(t)dt = \int_{T}^{+\infty}0dt = 0$$

If that doesn't work, than I don't know what would

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