Compute estimate of autoregressive (AR) model parameters using Burg method
Estimation / Parametric Estimation
dspparest3
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 LevinsonDurbin recursion.
The input is a samplebased vector (row, column, or 1D) or framebased vector (column only) representing a frame of consecutive time samples from a singlechannel signal, which is assumed to be the output of an AR system driven by white noise. The block computes the normalized estimate of the AR system parameters, A(z), independently for each successive input frame.
$$H(z)=\frac{G}{A(z)}=\frac{G}{1+a(2){z}^{1}+\dots +a(p+1){z}^{p}}$$
When you select the Inherit estimation order from input dimensions parameter, the order, p, of the allpole model is one less that 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 YuleWalker AR Estimator blocks.
Burg AR Estimator  Covariance AR Estimator  Modified Covariance AR Estimator  YuleWalker 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 LD 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 positivedefinite, hence nonsingular 
The realization to output, model coefficients, reflection coefficients, or both.
When selected, sets the estimation order p to one less than the length of the input vector.
The order of the AR model, p. This parameter is enabled when you do not select Inherit estimation order from input dimensions.
Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: PrenticeHall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: PrenticeHall, 1987.
Port  Supported Data Types 

Input 

A 

G 

Burg Method  DSP System Toolbox 
Covariance AR Estimator  DSP System Toolbox 
Modified Covariance AR Estimator  DSP System Toolbox 
YuleWalker AR Estimator  DSP System Toolbox 
arburg  Signal Processing Toolbox 