# What is power spectral density?

power spectral density (PSD), which describes how the power of a signal or time series is distributed with frequency. Here power can be the actual physical power, or more often, for convenience with abstract signals, can be defined as the squared value of the signal, that is, as the actual power if the signal was a voltage applied to a 1-ohm load.

Since a signal with nonzero average power is not square integrable, the Fourier transforms do not exist in this case. Fortunately, the Wiener-Khinchin theorem provides a simple alternative. The PSD is the Fourier transform of the autocorrelation function, R(τ), of the signal if the signal can be treated as a wide-sense stationary random process.

The power of the signal in a given frequency band can be calculated by integrating over positive and negative frequencies.

The power spectral density of a signal exists if and only if the signal is a wide-sense stationary process. If the signal is not stationary, then the autocorrelation function must be a function of two variables, so no PSD exists, but similar techniques may be used to estimate a time-varying spectral density.