In analyzing the frequency content of the signal x ( t ) , one might like to compute the ordinary Fourier transform x ^ ^ ( f ) ; however, for many signals of interest the Fourier transform does not formally exist. Regardless, Parseval's theorem tells us that we can re-write the average power as follows. P = lim T → → ∞ ∞ 1 T ∫ ∫ − − ∞ ∞ ∞ ∞ | x ^ ^ T ( f ) | 2 d f