Method for Reducing Noise in Data-Sets of Harmonic Signals

摘要

A method for reducing the noise in data-sets of harmonic signals that include data vectors X of length L, with each data vector X including P harmonic components is described. The method includes the steps of computing a Hankel matrix H by applying the equation (Hij)=(Xi+j−1); estimating a matrix Y by estimating the product of the Hankel matrix H by a matrix Ω, the matrix Ω including a set of K random unit vectors; computing an orthogonal matrix Q by performing a QR decomposition on the matrix Y and then computing the conjugate and transpose matrix Q* of the orthogonal matrix Q; estimating a K-ranked approximation {tilde over (H)} of the Hankel matrix H; and estimating (500) reduced noise data vectors X from the estimated K-ranked approximation {tilde over (H)} of the Hankel matrix H.

主权项

1. A method being performed on a computer for reducing the noise in large data-sets of harmonic signals comprising more than 105 points, the harmonic signals being represented as data vectors X of length L, each data vector X comprising P harmonic components, the method comprising the steps of:
computing a Hankel matrix H by applying the equation (Hij)=(Xi+j−1); estimating a matrix Y by estimating the product of the Hankel matrix H by a matrix Ω, said matrix Ω comprising a set of K random unit vectors; computing an orthogonal matrix Q by performing a QR decomposition on the matrix Y and then computing the conjugate and transpose matrix Q* of the orthogonal matrix Q; estimating a K-ranked approximation {tilde over (H)} of the Hankel matrix H; and, estimating reduced noise data vectors X from the estimated K-ranked approximation {tilde over (H)} of the Hankel matrix H.