Yule-Walker Method (DSP Blockset)

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

Library

Power Spectrum Estimation, in 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 spectrum is then computed from the FFT of the estimated AR model parameters.

The order of the all-pole model is specified by the Order parameter. The Yule-Walker Method and Burg Method blocks return similar results for large buffer lengths.

The input is a frame of consecutive time samples; a matrix input, u, is also treated as a single frame, u(:). The block's output is the estimate of the signal's power spectral density at N_fft equally spaced frequency points in the range [0,F_s), where N_fft is specified as a power of 2 by the FFT Size parameter and F_s is the signal's sample frequency. A value of -1 for FFT size instructs the block to use the input frame size as the FFT size. Otherwise, the block zero pads or truncates the input to N_fft before computing the FFT.

See the Burg Method block reference for a comparison of the Burg Method, Covariance Method, Modified Covariance Method, and Yule-Walker Method blocks.

Dialog Box

FFT length: The number of data points on which to perform the FFT, N_fft. If N_fft exceeds the size of the input frame, the data is zero padded as needed.
Order: The order of the AR model.

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.