A question asks for the energy and power of the following signal; $$x[n]=\text{sinc}\left(\frac{n}{5}\right)$$ given that $$\Omega_c=\pi/5$$ Energy is $$E=\sum_{n=-\infty}^{\infty}{\left |\text{sinc}\left(\frac{n}{5}\right)\right|^2}\rightarrow \frac{1}{2\pi}\int_{-\pi}^{\pi}\left|X_c(\Omega)\right|^2d\Omega$$ My resulting expression is $$E=\frac{1}{2\pi}\left(\frac{5}{\pi}\right)^2\int_{-\pi}^{\pi}\left|\frac{5}{\pi}\sum_{m=-\infty}^{\infty}{\text{p}\left(\frac{\Omega-2\pi m}{2\pi/5}\right)}\right|^2 d\Omega$$ Where p(t) is the UnitPulse function. How to simplify this expression?

  • $\begingroup$ Homework? Hint: Try to find a closed form solution for Xc(w) $\endgroup$
    – Hilmar
    Dec 11, 2013 at 12:00
  • $\begingroup$ Actually, depending on what is meant by "$p(t)$ is the UnitPulse function", is is worth considering that for any given number $\Omega$, at most one $m$ will make the argument of $p$ equal $)$ in that last displayed equation. $\endgroup$ Dec 11, 2013 at 22:09


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