# How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal

When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $$x(n)$$, does it make more sense to compute the energy as

$$E=\sum_1^N{x^2(n)}$$ over all the $$N$$ samples

or does it make more sense to compute the energy as the sum of the auto-correlation function values $$R_{xx}(k) = \sum_n {x(n+k) \, x(n)}$$ , which should be

$$E = \sum_k R_{xx}(k)$$ ?

Please let me know what you think about it.

Regards,

E.

• The first formula is the energy of one specific realization of the random signal. – MBaz Oct 14 '19 at 13:44
• I think that maybe the second formula cannot be applied, because it refers to a stationary signal ... any hint on how to extend the concept to non-stationary signals? – EmThorns Oct 14 '19 at 14:41
• Indeed. A quick web search revealed a few papers on this subject -- you may need to take a dive into the literature. – MBaz Oct 14 '19 at 15:48