3. Quick overview of spectral analysis methods

This section gives you a quick overview of the spectral analysis methods and classes that are available in spectrum. You will find the different classes associated to each PSD estimates. A functional approach is also possible but is not described here. See the reference guide for more details.

3.1. Non-parametric classes

The Fourier-based methods provides Periodogram, pcorrelogram, Welch estimate (not implemented see pylab.psd instead) and multitapering pmtm.

In addition to the Fourier-based methods, there are 3 types of non-parametric methods:

1. The Minimum of variance MV (Capon) is implemented in the class pminvar.
2. Two eigenvalues decomposition (MUSIC, eigenvalue) can be found in pev and pmusic.
3. Maximum entropy (MEM) (not yet implemented)

3.2. Autoregressive spectral estimation

There are essentially 3 methods to estimate the autoregressive (AR) parameters. The first one uses the autocorrelation sequence such as in the so-called Yule-Walker method (see pyule). A second method uses the reflection coefficient method such as in the Burg algorithm (see pburg). These methods minimise the forward prediction error (and backward) using Levinson recursion. Finally, a third important category of AR parameter method is based on the least squares linear prediction, which can be further decomposed into 2 categories. One that separate the minimization of the forward and backward linear prediction squared errors such as the autocorrelation or covariance methods (see pcovar). Another one that performs a combined minimization of the forward and backward prediction squared errors (modified covariance) (see pmodcovar).

Spectrum also provides parma, pma classes.