Do energy of signal and power spectrum (in db/hz) indicate towards same signal property? If I calculate energy of signal by squaring the magnitude of signal sample and power spectrum using spectrogram (db/hz) what kind of property of signal do they indicate and are they point towards same characterstic. That is higher energy signal will always have higher peak spectral power and vice versa. Also what is there practical significance.
On a straight forward approach, energy of a signal given by $E = \int \limits_{-\infty}^{+\infty}|x^2(t)|dt$ is a constant number whereas PSD can be obtained from FFT which is a function of frequency. PSD is the square of the absolute value of FFT.

In either case the value of energy or PSD gives an insight of the amplitude/strength of a signal.