Signal Processing Blockset™

Yule-Walker Method - Compute parametric estimate of tspectrum using Yule-Walker autoregressive (AR) method

Library

Estimation / Power Spectrum Estimation

dspspect3

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 you select Inherit estimation order from input dimensions, 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. To guarantee a valid output, you must set the Estimation order parameter to be less than or equal to half the input vector length. The spectrum is computed from the FFT of the estimated AR model parameters.

When you select Inherit FFT length from estimation order, N_fft is specified by (estimation order + 1), which must be a power of 2. When you do not select Inherit FFT length from estimation order, N_fft is specified as a power of 2 by the FFT length parameter, and the block zero pads or wraps 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 you do not select Inherit estimation order from input dimensions.

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_fft must be a power of 2, so (estimation order + 1) must be a power of 2.

FFT length

Enter the number of data points on which to perform the FFT, N_fft. When N_fft is larger than the input frame size, each frame is zero-padded as needed. When N_fft is smaller than the input frame size, each frame is wrapped as needed. This parameter is enabled when you clear the Inherit FFT length from input dimensions check box.

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.

Orfanidis, S. J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995.

Supported Data Types

The output data type is the same as the input data type.

See Also

See Power Spectrum Estimation for related information.

Yule-Walker IIR Filter Design (Obsolete)

Zero Crossing