Analytically determine a PSD from a transient function
Energy signals, i.e., signals with finite energy

$$\int_{-\infty}^{\infty}|f(t)|^2dt&lt;\infty$$

have zero power and, consequently, a power spectrum that is equal to zero. They do have an energy density spectrum, which is the squared magnitude of their Fourier transform.

You will only get a non-zero power spectrum, according to the definition in your question, for power signals, which have a finite non-zero power defined by

$$\overline{f^2(t)}=\lim_{T\to\infty}\frac{1}{T}\int_{-T/2}^{T/2}|f(t)|^2dt$$

I.e., power signals satisfy

$$0&lt;\overline{f^2(t)}&lt;\infty$$