Obtaining power spectrum from ACF, FFT using Matlab and FFTW
I am also confused about the terms power spectrum, power spectral density and energy spectrum. Are they used interchangeably? I would be grateful for an explanation of this phenomenon and normalization procedure.


EDIT with @jojek`s helpful comment: 

power spectrum is NOT the same as power spectral density despite the fact that terms are often mixed up. Units of power spectral density (PSD) are /Hz, e.g. /Hz. Power Spectrum (PS) is equal to PSD*(Equivalent Noise Bandwidth of used window funktion) and has units of  . You often normalise it with N, the number of data points (for discrete time series). For physical processes the PSD and PS are symmetric, thus negative frequencies contain no additional information and only positive frequencies are plotted, negative frequencies are discarded.

energy spectrum is a term of spectroscopy: it describes the intensity of a particle beam as a function of particle energy. What you maybe meant is called energy spectral density, which describes the distribution of energy over frequency; it has units of J/Hz

A good overview is here.

I want to add the term amplitude spectrum/amplitude spectral density, which is the square root of the power spectral density.