Spectral density estimation
Encyclopedia
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.
). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches
explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure.
Following is a partial list of spectral density estimation techniques:
Statistical signal processing
Statistical signal processing is an area of Applied Mathematics and Signal Processing that treats signals as stochastic processes, dealing with their statistical properties...
, the goal of spectral density estimation is to estimate
Estimation theory
Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the...
the spectral density
Spectral density
In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...
(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
Techniques for spectrum estimation can generally be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an auto-regressive or moving average modelAutoregressive moving average model
In statistics and signal processing, autoregressive–moving-average models, sometimes called Box–Jenkins models after the iterative Box–Jenkins methodology usually used to estimate them, are typically applied to autocorrelated time series data.Given a time series of data Xt, the ARMA model is a...
). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches
Non-parametric statistics
In statistics, the term non-parametric statistics has at least two different meanings:The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:...
explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure.
Following is a partial list of spectral density estimation techniques:
- PeriodogramPeriodogramThe periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898 as in the following quote:...
, a classic non-parametric technique - Autoregressive moving average estimation, based on fitting to an ARMA model
- MultitaperMultitaperIn signal processing, the multitaper method is a technique developed by David J. Thomson to estimate the power spectrum SX of a stationary ergodic finite-variance random process X, given a finite contiguous realization of X as data....
- Least-squares spectral analysisLeast-squares spectral analysisLeast-squares spectral analysis is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis...
, based on least-squares fitting to known frequencies