title: Scipy periodogram terminology confusion
body: <p>I am confused about the terminology used in scipy.signal.periodogram, namely:</p>
  
  <p>scaling : { 'density', 'spectrum' }, optional
          Selects between computing the power spectral density ('density')
          where <code>Pxx</code> has units of V*<em>2/Hz if <code>x</code> is measured in V and computing
          the power spectrum ('spectrum') where <code>Pxx</code> has units of V</em>*2 if <code>x</code> is
          measured in V. Defaults to 'density'</p>
  
  <p>(see: <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.periodogram.html" rel="noreferrer">http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.periodogram.html</a>)</p>
  
  <p>1) a few tests show that result for option 'density' is dependent on signal and window length and sampling frequency (grows when signal length increases). How come? I would say that it is exactly density that should be not dependent on these things. If I take a longer signal I should just get more accurate estimation, not different result. Not to mention that dependence on window length is also very surprising. 
  Result diverges in the limit of infinite signal, which could be a feature of energy, but not power. Shouldn't the periodogram converge to real theoretical PSD when length increases? If, so, am I supposed to perform another normalisation outside of the signal.periodogram method? </p>
  
  <p>2) to the contrary I see that alternative option 'spectrum' gives what I would previously call Power Spectrum Density, that is, it gives a resuls independent on window segment and window length and consistent with theoretical calculation. For instance for Asin(2PIft) a two sided solution yields two peaks at -f and f, each of height 0.25*A^2. </p>
  
  <p>There is a lot of literature on this subject, but I get an impression that also there is a lot of incompatibile terminology, so I will be thankful for any clarification. The straightforward question is how to interpret these options and their units. (I am used to seeing V^2/Hz which are labeled "Power Spectrum Density").</p>