Burg AR Estimator
Compute estimate of autoregressive (AR) model parameters using Burg method
Library
Estimation / Parametric Estimation
dspparest3
Description
The Burg AR Estimator block uses the Burg method to fit an autoregressive (AR) model to the input data by minimizing (least squares) the forward and backward prediction errors while constraining the AR parameters to satisfy the Levinson-Durbin recursion.
The input must be a column vector or an unoriented vector, which is assumed to be the output of an AR system driven by white noise. This input represents a frame of consecutive time samples from a single-channel signal. The block computes the normalized estimate of the AR system parameters, A(z), independently for each successive input frame.
When you select the Inherit estimation order from input dimensions parameter, the order, p, of the all-pole model is one less than the length of the input vector. Otherwise, the order is the value specified by the Estimation order parameter.
The Output(s) parameter allows you to select between two realizations of the AR process:
A— The top output, A, is a column vector of length p+1 with the same frame status as the input, and contains the normalized estimate of the AR model polynomial coefficients in descending powers of z.[1 a(2) ... a(p+1)]
K— The top output, K, is a column vector of length p with the same frame status as the input, and contains the reflection coefficients (which are a secondary result of the Levinson recursion).A and K— The block outputs both realizations.
The scalar gain, G, is provided at the bottom output
(G).
The following table compares the features of the Burg AR Estimator block to the Covariance AR Estimator, Modified Covariance AR Estimator, and Yule-Walker AR Estimator blocks.
| Burg AR Estimator | Covariance AR Estimator | Modified Covariance AR Estimator | Yule-Walker AR Estimator | |
|---|---|---|---|---|
Characteristics | Does not apply window to data | Does not apply window to data | Does not apply window to data | Applies window to data |
Minimizes the forward and backward prediction errors in the least squares sense, with the AR coefficients constrained to satisfy the L-D recursion | Minimizes the forward prediction error in the least squares sense | Minimizes the forward and backward prediction errors in the least squares sense | Minimizes the forward prediction error in the least squares sense (also called “autocorrelation method”) | |
| Always produces a stable model | Always produces a stable model | ||
| May produce unstable models | May produce unstable models | Performs relatively poorly for short data records | |
| Order must be less than or equal to half the input frame size | Order must be less than or equal to 2/3 the input frame size | Because of the biased estimate, the autocorrelation matrix is guaranteed to positive-definite, hence nonsingular |
Parameters
- Output(s)
The realization to output, model coefficients, reflection coefficients, or both.
- Inherit estimation order from input dimensions
When selected, sets the estimation order p to one less than the length of the input vector.
- Estimation order
The order of the AR model, p. This parameter is enabled when you do not select Inherit estimation order from input dimensions.
References
Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: Prentice-Hall, 1987.
Supported Data Types
| Port | Supported Data Types |
|---|---|
Input |
|
A |
|
G |
|
See Also
| Burg Method | DSP System Toolbox |
| Covariance AR Estimator | DSP System Toolbox |
| Modified Covariance AR Estimator | DSP System Toolbox |
| Yule-Walker AR Estimator | DSP System Toolbox |
arburg | Signal Processing Toolbox |