# reference parseval theorem limited signal

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

• 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? – MBaz Jul 15 '19 at 22:21
• @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. – Luca Mirtanini Jul 16 '19 at 7:50
• @LucaMirtanini what did you write in your report, exactly? – AlexTP Jul 16 '19 at 11:31
• @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 – Luca Mirtanini Jul 16 '19 at 12:02

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