# Yule-Walker Method

Power spectral density estimate using Yule-Walker method

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

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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

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

The block outputs are always nonsingular.

Data Types: `single` | `double`

## Parameters

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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.

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.

When you select the Inherit FFT length from estimation order parameter, the FFT length Nfft 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 Nfft before computing the FFT.

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

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.

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`

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## 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.

## Version History

Introduced before R2006a