User`s guide

Yule-Walker AR Estimator
5-546
5Yule-Walker AR Estimator
Purpose Compute an estimate of AR model parameters using the Yule-Walker method.
Library Estimation / Parametric Estimation
Description The Yule-Walker AR Estimator block uses the Yule-Walker AR method, also
called the autocorrelation method, to fit 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 the Levinson-Durbin recursion.
The Yule-Walker AR Estimator block can output the AR model coefficients as
polynomial coefficients, reflection coefficients, or both. 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,
which is assumed to be the output of an AR system driven by white noise. The
block computes the normalized estimate of the AR system parameters, A(z),
independently for each successive input frame.
When
Inherit estimation order from input dimensions is selected, the
order, p, of the all-pole model is one less that the length of the input vector.
Otherwise, the order is the value specified by the
Estimation order
parameter. The Yule-Walker AR Estimator and Burg AR Estimator blocks
return similar results for large frame sizes.
When
Output(s) is set to A, port A is enabled. Port A outputs a column vector
of length p+1 that contains the normalized estimate of the AR model
coefficients in descending powers of z,
[1 a(2) ... a(p+1)]
When Output(s) is set to K, port K is enabled. Port K outputs a length-p column
vector whose elements are the AR model reflection coefficients. When
Output(s) is set to A and K, both port A and K are enabled, and each port
outputs its respective column vector of AR model coefficients. The outputs at
both ports
A and K are always 1-D vectors.
The square of the model gain, G (a scalar), is provided at port
G.
Hz()
G
Az()
------------
G
1 a 2()z
1–
… ap 1+()z
p–
+++
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