# How do we calculate Power Spectrum Density (PSD) which is given in dB/Hz and not just dB?

I found many definitions for this quantity, PSD. In a document on signal analysis by National Instruments say that it is the amount of power in a unit bandwidth. Let's say P(f) is the power of the signal contained in a given frequency 'f', then the PSD at frequency $f_n$ is given by $\frac{\Sigma_{i-3}^{i+3}P(f_n)}{f_{i+3}-f_{i-3}}$ where $n \epsilon Z$ and has the units W/Hz or dB/Hz.

I came to know that Power spectrum gives the power contained in a particular frequency (W vs Hz) whereas PSD gives power contained in a unit bandwidth of the signal (W/Hz vs Hz). I realize that they are different but I am unable to figure out how to calculate it. One more thing to add, Gaussian white noise has its power equally spread over all the frequencies and so we expect it to have a constant value in the power spectrum. But we see that it has spikes at some particular values and it varies very much from the constant we expect while in a source I found online PSD remains constant over all frequencies for Gaussian white noise. This is shown in figure below.

I have also found that PSD is mostly used to study all types of noise like white noise, 1/f noise etc. My interest mainly lies in the difference of units between Powerspectrum and PSD which are given by W and W/Hz respectively. Please help me understand this concept if anybody comes across it.

• dB/Hz does not make a lot of sense, because integrating over that would not work. You need a linear scale in order to define a meaningful density. – Jazzmaniac Oct 16 '15 at 16:57
• The Fourier transform of white noise will contain spurious "spikes". What you need to do is averaging over several frames to get a good estimate of the PSD. – Emanuel Landeholm Oct 16 '15 at 20:26
• @EmanuelLandeholm By average we get the constant value but how do we go from W to W/Hz units or Power spectrum to PSD? – Pavan Oct 17 '15 at 5:08