# Energy Signals

1. Jan 24, 2012

### Axis001

1. The problem statement, all variables and given/known data

X(t) = Xe(t) + Xo(t) where Xe(t) = (1/2){X(t)+X(-t)} is the even part and Xo(t) = (1/2){X(t)-X(-t)} is the odd part of the signal. Let X(t) be an energy signal with energy 5 Joules. Suppose the even part of X(t) is Xe(t) = exp(-|t|). Determine the energy in Xo(t).

2. Relevant equations

E = ∫|X(t)|^2 dt from -infinity to infinity

3. The attempt at a solution

I have attempted this problem two ways.

First I tried to derive Xo(t) by using the above energy equation and substituting {Xe(t) + Xo(t)} with E = 5 J and from there I got the result Xo(t) = -exp(-|t|). Which didn't make sense since that would mean that X(t) = 0 but somehow has energy of 5 J.

My second attempt at this I started with the base equations provided for Xe(t) and set them equal to each other which resulted in X(-t) = 2exp(-|t|) + X(t). Taking this result and plugging it into the equation for Xo(t) again resulted in Xo(t) = -exp(-|t|). This again makes no sense.

I think I am simply over complicating this problem or I am just doing something very wrong. Either way any help would be greatly appreciated.