DSP Blockset    
Yule-Walker Method

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

Library

Estimation / Power Spectrum Estimation

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.

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 Nfft equally spaced frequency points in the range [0,Fs), where Fs 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 input dimensions is selected, Nfft is specified by the frame size of the input, which must be a power of 2. When Inherit FFT length from input dimensions is not selected, Nfft is specified as a power of 2 by the FFT length parameter, and the block zero pads or truncates the input to Nfft 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 Method blocks. The Yule-Walker Method 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 input dimensions
When selected, uses the input frame size as the number of data points, Nfft, on which to perform the FFT.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft exceeds the input frame size, the frame is zero-padded as needed. This parameter is enabled when Inherit FFT length 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.

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

See Power Spectrum Estimation for related information.


 Yule-Walker IIR Filter Design Zero Pad