| Signal Processing Toolbox | |
Spectral Estimation Method
The various methods of spectrum estimation available in the Signal Processing Toolbox can be categorized as follows:
Nonparametric methods are those in which the estimate of the PSD is made directly from the signal itself. The simplest such method is the periodogram. An improved version of the periodogram is Welch's method [8]. A more modern nonparametric technique is the multitaper method (MTM).
Parametric methods are those in which the signal whose PSD we want to estimate is assumed to be output of a linear system driven by white noise. Examples are the Yule-Walker autoregressive (AR) method and the Burg method. These methods estimate the PSD by first estimating the parameters (coefficients) of the linear system that hypothetically "generates" the signal. They tend to produce better results than classical nonparametric methods when the data length of the available signal is relatively short.
Subspace methods, also known as high-resolution methods or super-resolution methods, generate frequency component estimates for a signal based on an eigenanalysis or eigendecomposition of the correlation matrix. Examples are the multiple signal classification (MUSIC) method or the eigenvector (EV) method. These methods are best suited for line spectra - that is, spectra of sinusoidal signals - and are effective in the detection of sinusoids buried in noise, especially when the signal to noise ratios are low.
All three categories of methods are listed in the table below with the corresponding toolbox function names. More information about each function is on the corresponding function reference page. See Parametric Modeling for details about lpc and other parametric estimation functions.
| Method |
Description |
Functions |
| Periodogram |
Power spectral density estimate |
|
| Welch |
Averaged periodograms of overlapped, windowed signal sections |
pwelch, csd, tfe, cohere |
| Multitaper) |
Spectral estimate from combination of multiple orthogonal windows (or "tapers") |
|
| Yule-Walker AR |
Autoregressive (AR) spectral estimate of a time-series from its estimated autocorrelation function |
|
| Burg |
Autoregressive (AR) spectral estimation of a time-series by minimization of linear prediction errors |
|
| Covariance |
Autoregressive (AR) spectral estimation of a time-series by minimization of the forward prediction errors |
|
| Modified Covariance |
Autoregressive (AR) spectral estimation of a time-series by minimization of the forward and backward prediction errors |
|
| MUSIC |
Multiple signal classification |
|
| Eigenvector |
Pseudospectrum estimate |
|
| | Spectral Analysis | Nonparametric Methods | |