The two concepts are, however, closely related, and it is possible to convert from one to the other: For example, if x(t) represents the potential (in volts) of an electrical signal propagating across a transmission line, then Z would represent the characteristic impedance (in ohms) of the transmission line.
would appear as volt2·seconds, which is not dimensionally correct for energy in the sense of the physical sciences.
which is equivalent to joules, the SI unit for energy as defined in the physical sciences.
Similarly, the spectral energy density of signal x(t) is where X(f) is the Fourier transform of x(t).
would represent the signal's spectral energy density (in volts2·second2 per meter2) as a function of frequency f (in hertz).
Again, these units of measure are not dimensionally correct in the true sense of energy density as defined in physics.
by Zo, the characteristic impedance of free space (in ohms), the dimensions become joule-seconds per meter2 or, equivalently, joules per meter2 per hertz, which is dimensionally correct in SI units for spectral energy density.