So yeah, I have $f(t)=e^{-t}H(t-\frac{1}{2})$ and I want to calculate its energy and what $\omega$ range holds 95% of the signal's total energy. I know that I'm probably going to use Parseval and time shift to make the function integral range from $0$ to $inf$, but I'm not quite sure as to how.
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1$\int_{-\infty}^\infty |f(t)|^2 dt = \int_{1/2}^\infty e^{-2t}dt = , ?$ Then what did you find for $\hat{f}(\omega)$ ? – reuns Feb 21 '17 at 21:22
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Energy at $E=\frac{1}{2e}-\frac{1}{2}$ and FT $\frac{ie^{-\frac{1}{2}-\frac{1}{2}i\omega}}{\omega -i}$ – Grak Feb 22 '17 at 05:55
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E at $\frac{1}{2e}$ I mean – Grak Feb 22 '17 at 06:01
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So that $|\hat{f}(\omega)|^2 = ?$ and $\int_{-A}^A |\hat{f}(\omega)|^2 d\omega = ?$ – reuns Feb 22 '17 at 08:59