Academic help online

Hebbian-Based Maximum Eigenfilter
For the matched filter considered in Example 2, the eigenvalue 1 and associated eigenvector q1 are respectively defined by

Example 2
Consider a random vector X, a realization of which is denoted by the sample vector x. Let

where the vector s, representing the signal component, is fixed with a Euclidean norm of one.The random vector V, representing the additive noise component, has zero mean and covariance matrix σ2I. The correlation matrix of X is given by

The largest eigenvalue of the correlation matrix R is therefore

The associated eigenvector q1 is equal to s. It is readily shown that this solution satisfies the eigenvalue problem

Hence, for the situation described in this example, the self-organized linear neuron (upon convergence to its stable condition) acts as a matched filter in the sense that its impulse response (represented by the synaptic weights) is matched to the signal component s.

All Rights Reserved,
Disclaimer: You will use the product (paper) for legal purposes only and you are not authorized to plagiarize. In addition, neither our website nor any of its affiliates and/or partners shall be liable for any unethical, inappropriate, illegal, or otherwise wrongful use of the Products and/or other written material received from the Website. This includes plagiarism, lawsuits, poor grading, expulsion, academic probation, loss of scholarships / awards / grants/ prizes / titles / positions, failure, suspension, or any other disciplinary or legal actions. Purchasers of Products from the Website are solely responsible for any and all disciplinary actions arising from the improper, unethical, and/or illegal use of such Products.