Yule-Walker Method (DSP Blockset)

Compute a parametric estimate of the spectrum using the Yule-Walker AR method.

Library

Description

The Yule-Walker Method block estimates the power spectral density (PSD) of the input using the Yule-Walker AR method. This method, also called the autocorrelation method, fits 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 Levinson-Durbin recursion. Block outputs are always nonsingular.

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. The block's output (a column vector) is the estimate of the signal's power spectral density at N_fft equally spaced frequency points in the range [0,F_s), where F_s is the signal's sample frequency.

When Inherit estimation order from input dimensions is selected, the order of the all-pole model is one less that the input frame size. Otherwise, the order is the value specified by the Estimation order parameter. The spectrum is computed from the FFT of the estimated AR model parameters.

When Inherit FFT length from estimation order is selected, N_fft is specified by (estimation order + 1), which must be a power of 2. When Inherit FFT length from estimation order is not selected, N_fft is specified as a power of 2 by the FFT length parameter, and the block zero pads or truncates the input to N_fft before computing the FFT. The output is always sample-based.

See the Burg Method block reference for a comparison of the Burg Method, Covariance Method, Modified Covariance Method, and Yule-Walker AR Estimator blocks. The Yule-Walker AR Estimator and Burg Method blocks return similar results for large buffer lengths.

Dialog Box

Inherit estimation order from input dimensions: When selected, sets the estimation order to one less than the length of the input vector.
Estimation order: The order of the AR model. This parameter is enabled when Inherit estimation order from input dimensions is not selected.
Inherit FFT length from estimation order: When selected, uses the estimation order to determine the number of data points, N_fft, on which to perform the FFT. Sets N_fft equal to (estimation order + 1). Note that N_fftmust be a power of 2, so (estimation order + 1) must be a power of 2.
FFT length: The number of data points, N_fft, on which to perform the FFT. If N_fft exceeds the input frame size, the frame is zero-padded as needed. This parameter is enabled when Inherit FFT length from estimation order 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 Method
DSP Blockset

Covariance Method
DSP Blockset

Levinson-Durbin
DSP Blockset

Autocorrelation LPC
DSP Blockset

Short-Time FFT
DSP Blockset

Yule-Walker AR Estimator
DSP Blockset

pyulear
Signal Processing Toolbox

Burg Method	DSP Blockset
Covariance Method	DSP Blockset
Levinson-Durbin	DSP Blockset
Autocorrelation LPC	DSP Blockset
Short-Time FFT	DSP Blockset
Yule-Walker AR Estimator	DSP Blockset
`pyulear`	Signal Processing Toolbox

See Power Spectrum Estimation for related information. Also see a list of all blocks in the Power Spectrum Estimation library.

Yule-Walker AR Estimator Zero Pad