Power spectral density - Definition and Overview

In physics, the spectral density, or more correctly the power spectral density (PSD) of a given bandwidth of electromagnetic radiation is the total power in this bandwidth divided by the specified bandwidth.

Spectral density is usually expressed in watts per hertz (W/Hz).

There exist both power and energy spectral densities. The energy spectral density is defined as

<math>\Psi_x(f) = \left| X(f) \right|^2.<math>

Note that the total energy in the frequency domain equals the total energy in the time domain:

<math> \int \left| x(t) \right|^2\, dt = \int \Psi_x(f)\, df. <math>

This is a result of Parseval's theorem.

Practically, for discrete-time signals, the PSD is calculated using the FFT. One example is Welch's method.