LevinsonDurbin

VisualSim.actor.lib
Class LevinsonDurbin

• public class LevinsonDurbin
• extends TypedAtomicActor

• This actor uses the Levinson-Durbin algorithm to compute the linear predictor coefficients of a random process, given its autocorrelation function as an input. These coefficients are produced both in tapped delay line form (on the linearPredictor output) and in lattice filter form (on the reflectionCoefficients output). The order of the predictor (the number of linearPredictor and coefficients reflectionCoefficients produced) is the number of lags of the supplied autocorrelation. The errorPower output is the power of the prediction error as a function of the predictor order. The inputs and outputs are all arrays of doubles.

The autocorrelation estimates provided as inputs can be generated by the Autocorrelation actor. It the Autocorrelation actor is set so that its biased parameter is true, then the combined effect of that actor and this one is called the autocorrelation method. The order of the predictor is the value of the numberOfLags parameter of the Autocorrelation actor. If the length of the autocorrelation input is odd, then it is assumed to be a symmetric autocorrelation function, and the order of the predictor calculated by this actor is (length + 1)/2. Otherwise, the order is 1 + (length/2), which assumes that discarding the last sample of the autocorrelation would make it symmetric.

Three output signals are generated by this actor. On the errorPower output port, an array of length order + 1 gives the prediction error power for each predictor order from zero to order. The first value in this array, which corresponds to the zeroth-order predictor, is simply the zero-th lag of the input autocorrelation, which is the power of the random process with that autocorrelation. Note that for signals without noise whose autocorrelations are estimated by the Autocorrelation actor, the errorPower output can get small. If it gets close to zero, or goes negative, this actor fixes it at zero. "Close to" is determined by the close() method of the VisualSim.math.SignalProcessing class.

The linearPredictor output gives the coefficients of an FIR filter that performs linear prediction for the random process. This set of coefficients is suitable for directly feeding a VariableFIR actor, which accepts outside coefficients. The number of coefficients produced is equal to the order. The predictor coefficients produced by this actor can be used to create a maximum-entropy spectral estimate of the input to the Autocorrelation actor. They can also be used for linear-predictive coding, and any number of other applications.

The reflectionCoefficients output is the reflection coefficients, suitable for feeding directly to a VariableLattice actor, which will then generate the forward and backward prediction error. The number of coefficients produced is equal to the order.

Note that the definition of reflection coefficients is not quite universal in the literature. The reflection coefficients in reference [2] is the negative of the ones generated 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.

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.

• Version:
• $Id: LevinsonDurbin.java,v 1.11 2003/01/08 01:21:39
•  
• See Also:
• VisualSim.simulators.sdf.lib.Autocorrelation
• VisualSim.simulators.sdf.lib.VariableFIR
• VisualSim.simulators.sdf.lib.VariableLattice
• VisualSim.math.SignalProcessing
•  

autocorrelation

public TypedIOPort autocorrelation

• The autocorrelation input, which is an array.

errorPower

public TypedIOPort errorPower

• The output for the error power, as a function of the predictor order. This produces an array.

linearPredictor

public TypedIOPort linearPredictor

• The output for linear predictor coefficients. This produces an array.

reflectionCoefficients

public TypedIOPort reflectionCoefficients

• The output for lattice filter coefficients for a prediction error filter. This produces an array.

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