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.