A recursive (all-pole) filter with a lattice structure.
The coefficients of such a filter are called "reflection coefficients."
Recursive lattice filters are typically used as synthesis filters for
random processes because it is easy to ensure that they are stable.
A recursive lattice filter is stable 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.
<p>
The default reflection coefficients correspond to the following
transfer function:
<pre>
1
H(z) = --------------------------------------
1 - 2z<sup>-1</sup> + 1.91z<sup>-2</sup> - 0.91z<sup>-3</sup> + 0.205z<sup>-4</sup>
</pre>
<p>
The structure of the filter is as follows:
<pre>
y[0] y[1] y[n-1] y[n]
X(n) ---(+)->--o-->----(+)->--o--->-- ... ->--(+)->--o--->---o---> Y(n)
\ / \ / \ / |
+Kn / +Kn-1 / +K1 / |
X X X |
-Kn \ -Kn-1 \ -K1 \ V
/ \ / \ / \ |
(+)-<--o--[z]--(+)-<--o--[z]- ... -<--(+)-<--o--[z]--/
w[1] w[2] w[n]
</pre>
where the [z] are unit delays and the (+) are adders
and "y" and "w" are variables representing the state of the filter.
<p>
The reflection (or partial-correlation (PARCOR))
coefficients should be specified
right to left, K1 to Kn as above.
Using exactly the same coefficients in the
Lattice actor will result in precisely the inverse transfer function.
<p>
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.
<p>
<b>References</b>
<p>[1]
J. Makhoul, "Linear Prediction: A Tutorial Review",
<i>Proc. IEEE</i>, Vol. 63, pp. 561-580, Apr. 1975.
<p>[2]
S. M. Kay, <i>Modern Spectral Estimation: Theory & Application</i>,
Prentice-Hall, Englewood Cliffs, NJ, 1988.
Edward A. Lee, Christopher Hylands, Steve Neuendorffer
$Id: RecursiveLattice.java 70402 2014-10-23 00:52:20Z cxh $
Ptolemy II 1.0
Yellow (cxh)
Yellow (cxh)
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.