Spectral density estimation

In statistical signal processing, the goal of spectral density estimation is to estimate the spectral density (also known as the power spectrum) of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. The purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

Techniques
Almost all the techniques that estimate the power spectrum rely on a smoothed version of a Fourier transform of the random observations. There are parametric approaches that assume that the underlying stationary stochastic process is described parametrically (for example using an auto-regressive or moving average model). In these parametric approaches, the task is to estimate the parameters of the model that describes the stochastic process. There are also non-parametric approaches, which explicitly estimate the covariance or the spectrum of the process.

Following is a partial list of spectral density estimation techniques:
 * Periodogram, a classic non-parametric technique
 * Autoregressive moving average estimation, based on fitting to an ARMA model
 * Least-squares spectral analysis, based on least-squares fitting to known frequencies