Development and analysis of a neural network approach to Pisarenko's harmonic retrieval method

The authors recast a known constrained minimization formulation for obtaining an appropriate energy function for the neural network (NN) framework using the penalty function approach and show that the required eigenvector is a minimizer of this energy function.

Abstract

Pisarenko's harmonic retrieval (PHR) method is perhaps the first eigenstructure based spectral estimation technique. The basic step in this method is the computation of eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix of the underlying data. The authors recast a known constrained minimization formulation for obtaining this eigenvector into the neural network (NN) framework. Using the penalty function approach, they develop an appropriate energy function for the NN. This NN is of feedback type with the neurons having sigmoidal activation function. Analysis of the proposed approach shows that the required eigenvector is a minimizer (with a given norm) of this energy function. Further, all its minimizers are global minimizers. Bounds on the integration time step that is required to numerically solve the system of nonlinear differential equations, which define the network dynamics, have been derived. Results of computer simulations are presented to support their analysis.>