Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

In my signals assignment, I'm asked to show that, for a continuous time, real-valued signal x(t):

Ex_even = Ex_odd = 0.5 * Ex

So here's what I've done:

Ex_even = ∫|(x(t) + x(-t))/2|²dt

Ex_even = 0.5 * ∫|(x(t)² + 2x(t)x(-t) + x(-t)²)/2|dt

Ex_even = 0.5 * [ 0.5 * ∫x(t)²dt + ∫x(t)x(-t)dt + 0.5 * ∫x(-t)²dt ]

Now, I assume that ∫x(t)x(-t)dt must go to zero (when integrated from -∞ to +∞), but I don't understand why. Could someone explain it to me?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Energy of even & odd signals

**Physics Forums | Science Articles, Homework Help, Discussion**