Yule-Walker AR Estimator (DSP Blockset)

Compute an estimate of AR model parameters using the Yule-Walker method.

Library

Description

The Yule-Walker AR Estimator block uses the Yule-Walker AR method, also called the autocorrelation method, to fit an autoregressive (AR) model to the windowed input data by minimizing the forward prediction error in the least-squares sense. This formulation leads to the Yule-Walker equations, which are solved by the Levinson-Durbin recursion. Block outputs are always nonsingular.

The Yule-Walker AR Estimator block can output the AR model coefficients as polynomial coefficients, reflection coefficients, or both. The input is a sample-based vector (row, column, or 1-D) or frame-based vector (column only) representing a frame of consecutive time samples from a single-channel 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.

When Inherit estimation order from input dimensions is selected, 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 Yule-Walker AR Estimator and Burg AR Estimator blocks return similar results for large frame sizes.

When Output(s) is set to A, port A is enabled. Port A outputs a column vector of length p+1 that contains the normalized estimate of the AR model coefficients in descending powers of z,

```
[1 a(2) ... a(p+1)]
```

When Output(s) is set to K, port K is enabled. Port K outputs a length-p column vector whose elements are the AR model reflection coefficients. When Output(s) is set to A and K, both port A and K are enabled, and each port outputs its respective column vector of AR model coefficients. The outputs at both ports A and K are always 1-D vectors.

The square of the model gain, G (a scalar), is provided at port G.

Dialog Box

Output(s): The type of AR model coefficients output by the block. The block can output polynomial coefficients (A), reflection coefficients (K), or both (A and K). Tunable.
Inherit estimation order from input dimensions: When selected, sets the estimation order p to one less than the length of the input vector. Tunable.
Estimation order: The order of the AR model, p. This parameter is enabled when Inherit estimation order from input dimensions is not selected.

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

Double-precision floating point
Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Burg AR Estimator
DSP Blockset

Covariance AR Estimator
DSP Blockset

Modified Covariance AR Estimator
DSP Blockset

Yule-Walker Method
DSP Blockset

aryule
Signal Processing Toolbox

Burg AR Estimator	DSP Blockset
Covariance AR Estimator	DSP Blockset
Modified Covariance AR Estimator	DSP Blockset
Yule-Walker Method	DSP Blockset
`aryule`	Signal Processing Toolbox

Also see Parametric Estimation for a list of all the blocks in the Parametric Estimation library.

Window Function Yule-Walker Method