Yule-Walker Method

Power spectral density estimate using Yule-Walker method

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Libraries:
DSP System Toolbox / 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 process leads to the Yule-Walker equations, which the Levinson-Durbin recursion solves.

The block computes the spectrum from the FFT of the estimated AR model parameters.

Ports

Input

Input — Input

column vector | unoriented vector

Specify the input as a column vector or an unoriented vector. This input represents a frame of consecutive time samples from a single-channel signal.

Data Types: single | double

Output

Output — Power spectral density estimate

column vector

Power spectral density estimate of the signal at N_fft equally spaced frequency points, returned as a column vector. The frequency points are in the range [0,F_s), where F_s is the sampling rate of the signal.

The block outputs are always nonsingular.

Data Types: single | double

Parameters

Inherit estimation order from input dimensions — Inherit estimation order from input dimensions

off (default) | on

When you select Inherit estimation order from input dimensions parameter, the block sets the order of the all-pole model (estimation order) to a value that is one less than the length of the input frame size. Otherwise, the Estimation order parameter value specifies the order. The block computes the spectrum from the FFT of the estimated AR model parameters.

Estimation order — Order of AR model

6 (default) | nonnegative integer

Specify the estimation order of the AR model as a nonnegative integer. To guarantee a valid output, the Estimation order parameter must be less than or equal to 1/2 the input vector length.

Dependencies

To enable this parameter, clear the Inherit estimation order from input dimensions parameter.

Inherit FFT length from estimation order — Inherit FFT length from estimation order

off (default) | on

When you select the Inherit FFT length from estimation order parameter, the FFT length N_fft is one greater than the estimation order. To specify the number of points on which to perform the FFT, clear the Inherit FFT length from estimation order parameter. You can then specify the FFT length as a power of 2 using the FFT length parameter. The block zero-pads or wraps the input to N_fft before computing the FFT.

FFT length — FFT length

256 (default) | positive integer greater than or equal to 2

Enter the number of data points N_fft on which to perform the FFT as a positive integer greater than or equal to 2. When N_fft is larger than the input frame size, the block zero-pads each frame as needed. When N_fft is smaller than the input frame size, the block wraps each frame as needed.

Dependencies

To enable this parameter, clear the Inherit FFT length from input dimensions parameter.

Inherit sample time from input — Inherit sample time from input

on (default) | off

When you select the Inherit sample time from input parameter, the block computes the frequency data from the sample period of the input signal. For the block to produce a valid output, the following conditions must hold:

• The input to the block is the original signal with no samples added or deleted (by insertion of zeros, for example).

• The sample period of the time-domain signal in the simulation equals the sample period of the original time series.

If these conditions do not hold, clear the Inherit sample time from input check box. You can then specify a sample time using the Sample time of original time series parameter.

Sample time of original time series — Sample time of original time-domain signal

1 (default) | positive scalar

Specify the sample time of the original time-domain signal as a positive scalar.

Dependencies

To enable this parameter, clear the Inherit sample time from input parameter.

Block Characteristics

Data Types	double | single
Multidimensional Signals	No
Variable-Size Signals	No

More About

Compare Power Spectral Density Estimation Methods

The Burg Method and Yule-Walker Method blocks return similar results for large frame sizes.

This table compares the features of the Burg Method block to the Covariance Method, Modified Covariance Method, and the Yule-Walker Method blocks.

	Burg	Covariance	Modified Covariance	Yule-Walker
Characteristics	Does not apply window to data	Does not apply window to data	Does not apply window to data	Applies window to data
	Minimizes the forward and backward prediction errors in the least squares sense, with the AR coefficients constrained to satisfy the L-D recursion	Minimizes the forward prediction error in the least squares sense	Minimizes the forward and backward prediction errors in the least squares sense	Minimizes the forward prediction error in the least squares sense (also called autocorrelation method)
Advantages	High resolution for short data records	Better resolution than Yule-Walker for short data records (more accurate estimates)	High resolution for short data records	Performs as well as other methods for large data records
	Always produces a stable model	Able to extract frequencies from data consisting of p or more pure sinusoids	Able to extract frequencies from data consisting of p or more pure sinusoids	Always produces a stable model
			Does not suffer spectral line-splitting
Disadvantages	Peak locations highly dependent on initial phase	Can produce unstable models	Can produce unstable models	Performs relatively poorly for short data records
	Can suffer spectral line-splitting for sinusoids in noise, or when order is very large	Frequency bias for estimates of sinusoids in noise	Peak locations slightly dependent on initial phase	Frequency bias for estimates of sinusoids in noise
	Frequency bias for estimates of sinusoids in noise		Minor frequency bias for estimates of sinusoids in noise
Conditions for Nonsingularity		Order must be less than or equal to 1/2 the input frame size	Order must be less than or equal to 2/3 the input frame size	Because of the biased estimate, the autocorrelation matrix is guaranteed to be positive-definite, hence nonsingular

References

[1] Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.

[2] Marple, S. L. Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: Prentice-Hall, 1987.

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a