User`s guide

Levinson-Durbin
5-265
The prediction error power, P, (a scalar), is output when the Output
prediction error power (P)
check box is selected. P represents the power of
the output of an FIR filter with taps A and input autocorrelation described by
r, where A represents a prediction error filter and r is the input to the block.
(In this case, A is a whitening filter).
When
If the value of lag 0 is zero, A=[1 zeros], K=[zeros], P=0 is selected
(default), an input whose
r(1) element is zero generates a zero-valued output.
When this check box is not selected, an input with
r(1) = 0 generates NaNs in
the output. In general, an input with
r(1) = 0 is invalid because it does not
construct a positive-definite matrix R; however, it is common for blocks to
receive zero-valued inputs at the start of a simulation. The check box allows
you to avoid propagating
NaNs during this period.
Applications
One application of the Levinson-Durbin formulation above is in the
Yule-Walker AR problem, which concerns modeling an unknown system as an
autoregressive process. Such a process would be modeled as the output of an
all-pole IIR filter with white Gaussian noise input. In the Yule-Walker
problem, the use of the signal’s autocorrelation sequence to obtain an optimal
estimate leads to an Ra = b equation of the type shown above, which is most
efficiently solved by Levinson-Durbin recursion. In this case, the input to the
block represents the autocorrelation sequence, with
r(1) being the zero-lag
value. The output at the block’s
A port then contains the coefficients of the
autoregressive process that optimally models the system. The coefficients are
ordered in descending powers of z, and the AR process is minimum phase. The
prediction error, G, defines the gain for the unknown system, where .
The output at the block’s
K port contains the corresponding reflection
coefficients,
[k(1) k(2) ... k(n)], for the lattice realization of this IIR filter.
The Yule-Walker AR Estimator block implements this autocorrelation-based
method for AR model estimation, while the Yule-Walker Method block extends
the method to spectral estimation.
Another common application of the Levinson-Durbin algorithm is in linear
predictive coding, which is concerned with finding the coefficients of a moving
GP=
Hz()
G
Az()
------------
G
1 a 2()z
1–
… an 1+()z
n–
+++
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