The energy spectral density is most suitable for transients—that is, pulse-like signals—having a finite total energy. Finite or not, Parseval's theorem (or Plancherel's theorem) gives us an alternate expression for the energy of the signal: ∫ ∫ − − ∞ ∞ ∞ ∞ | x ( t ) | 2 d t = ∫ ∫ − − ∞ ∞ ∞ ∞ | x ^ ^ ( f ) | 2 d f , where: x ^ ^ ( f ) ≜ ≜ ∫ ∫ − − ∞ ∞ ∞ ∞ e − − i 2 π π f t x ( t ) d t is the value of the Fourier transform of x ( t ) at frequency f (in Hz). The theorem also holds true in the discrete-time cases. Since the integral on the left-hand side is the energy of the signal, the value of | x ^ ^ ( f ) | 2 d f can be interpreted as a density function multiplied by an infinitesimally small frequency interval, describing the energy contained in the signal at frequency f in the frequency interval f + d f .