# Burg AR Estimator

Compute estimate of autoregressive (AR) model parameters using Burg method

Libraries:
DSP System Toolbox / Estimation / Parametric Estimation

## 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.

## Ports

### Input

expand all

Specify the input data as a column vector or an unoriented vector. The block assumes that the input data is the output of an AR system driven by white noise and represents a frame of consecutive time samples from a single-channel signal.

Data Types: `single` | `double`

### Output

expand all

Normalized estimate of the AR model polynomial coefficients A(z), returned as a column vector of length p+1 in descending powers of z.

The block computes the estimate of these coefficients independently for each successive input frame.

`$H\left(z\right)=\frac{G}{A\left(z\right)}=\frac{G}{1+a\left(2\right){z}^{-1}+\dots +a\left(p+1\right){z}^{-p}}$`

where,

• H(z) –– Transfer function of the estimated AR model

• G –– Scalar gain

• A(z) –– Polynomial coefficients of the AR model

#### Dependency

To enable this port, set the Output(s) parameter to `A` or ```A and K```.

Data Types: `single` | `double`

Reflection coefficients (which are a secondary result of the Levinson recursion), returned as a column vector of length p.

#### Dependency

To enable this port, set the Output(s) parameter to `K` or ```A and K```.

Data Types: `single` | `double`

Gain of the estimated AR model, returned as a scalar.

`$H\left(z\right)=\frac{G}{A\left(z\right)}=\frac{G}{1+a\left(2\right){z}^{-1}+\dots +a\left(p+1\right){z}^{-p}}$`

where,

• H(z) –– Transfer function of the estimated AR model

• G –– Scalar gain

• A(z) –– Polynomial coefficients of the AR model

Data Types: `single` | `double`

## Parameters

expand all

Specify whether the block outputs model coefficients (`A`), reflection coefficients (`K`), or both (`A and K`).

When you select the Inherit estimation order from input dimensions parameter, the block sets the order p of the all-pole model to a value that is one less than the length of the input vector. Otherwise, the order is the value you specify in the Estimation order parameter.

Specify the order of the AR model p as a nonnegative integer.

#### Dependency

To enable this parameter, clear the Inherit estimation order from input dimensions parameter.

## Block Characteristics

 Data Types `double` | `single` Multidimensional Signals `No` Variable-Size Signals `No`

expand all

## Algorithms

Burg's method estimates the reflection coefficients and uses the reflection coefficients to estimate the AR parameters recursively. You can find the recursion and lattice filter relations describing the update of the forward and backward prediction errors in [1].

## References

[1] Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.

[2] Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: Prentice-Hall, 1987.

## Version History

Introduced before R2006a