DSP Blockset |

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 N_{fft} equally spaced frequency points in the range [0,F_{s}), where F_{s} 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, N_{fft} 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, N_{fft} is specified as a power of 2 by the **FFT length** parameter, and the block zero pads or truncates 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 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, N
_{fft}, on which to perform the FFT. **FFT length**- The number of data points, N
_{fft}, on which to perform the FFT. If N_{fft}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 |