
Lattice |
ptolemy.actor.lib.Lattice |
An FIR filter with a lattice structure. The coefficients of such a
filter are called "reflection coefficients." Lattice filters are
typically used as linear predictors because it is easy to ensure that
they are minimum phase, and hence that their inverse is stable.
A lattice filter is (strictly) minimum phase if its reflection
coefficients are all less than unity in magnitude. To get the
reflection coefficients for a linear predictor for a particular
random process, you can use the LevinsonDurbin actor.
The inputs and outputs are of type double.
The default reflection coefficients correspond to the optimal linear
predictor for an AR process generated by filtering white noise with
the following filter:
1
H(z) = --------------------------------------
1 - 2z-1 + 1.91z-2 - 0.91z-3 + 0.205z-4
Since this filter is minimum phase, the transfer function of the lattice
filter is H -1(z).
Note that the definition of reflection coefficients is not quite universal
in the literature. The reflection coefficients in reference [2]
are the negative of the ones used by this actor, which
correspond to the definition in most other texts,
and to the definition of partial-correlation (PARCOR)
coefficients in the statistics literature.
The signs of the coefficients used in this actor are appropriate for values
given by the LevinsonDurbin actor.
The structure of the filter is as follows:
y[0] y[1] y[n-1] y[n]
X(n) -------o-->-(+)-->----o-->-(+)-->-- ... ->---o-->-(+)------> Y(n)
| \ / \ / \ /
| +K1 / +K2 / +Kn /
| X X X
V -K1 \ -K2 \ -Kn \
| / \ / \ / \
\-[z]--o-->-(+)-[z]---o-->-(+)-[z]- ... ->---o-->-(+)
w[0] w[1] w[n-1] w[n]
References
[1]
J. Makhoul, "Linear Prediction: A Tutorial Review",
Proc. IEEE, Vol. 63, pp. 561-580, Apr. 1975.
[2]
S. M. Kay, Modern Spectral Estimation: Theory & Application,
Prentice-Hall, Englewood Cliffs, NJ, 1988.
Author(s): Edward A. Lee, Christopher Hylands, Steve Neuendorffer
Version:$Id: Lattice.java,v 1.33 2005/10/28 20:14:47 cxh Exp $
Pt.Proposed Rating:Yellow (eal)
Pt.Accepted Rating:Yellow (cxh)
reflectionCoefficients
The reflection coefficients. This is an array of doubles with
default value {0.804534, -0.820577, 0.521934, -0.205}. These
are the reflection coefficients for the linear predictor of a
particular random process.