What the Three Words Mean

June 25, 2019

Each of the three words in “power spectral density” represents an essential component of PSD analysis.

  • Power refers to the magnitude of the PSD. The magnitude is the mean-square value of the signal being analyzed. “Power” does not refer to a physical quantity of power like watts or horsepower. Power is proportional to the mean-square value of some quantity such as the square of current or voltage in an electrical circuit. Therefore, the mean-square value of any quantity is known as the “power” of the quantity.
  • Spectral refers to the PSD function of frequency. Just as a rainbow represents the distribution of light over a spectrum of wavelengths, PSD represents the distribution of a signal over a spectrum of frequencies. The next lesson details how a signal is converted from the time domain into the frequency domain during PSD calculation.
  • Density refers to the magnitude of the PSD normalized to a single hertz bandwidth. For example, if a signal measures acceleration in units G, the PSD has a unit of G2/Hz.

As the name “power spectral density” does not include the quantity being measured, the word “power” is sometimes replaced by the name of the quantity being measured. For example, the PSD of an acceleration signal is sometimes referred to as the acceleration spectral density.