# How to determine the power of a finite signal?

I am trying to write mathematically how to calculate the power of a finite signal. I know the general formula $$P_{\mathrm{x}}=\lim_{T\to\infty} \frac{1}{T} \int_{t=0}^{T} x^{2}(t) \mathrm{d} t$$ used to calculate the power of a signal which has infinite Energy and finite power. But how do you express it when the does not go to infinity, is not period and does not have infinite energy?

I know its a basic but i have searched all over and have not been able to find a proper answer.

First of all, note that your formula for signal power is only valid for real-valued $$x(t)$$ that satisfy $$x(t)=0$$ for $$t<0$$.
$$P_x=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{T}|x(t)|^2dt\tag{1}$$
$$E_x=\int_{-\infty}^{\infty}|x(t)|^2dt\lt\infty\tag{2}$$
the power $$P_x$$ defined by $$(1)$$ is clearly zero.