Central differenec quotient spectrum of singular value and its application on signal denoising

Abstract

Aiming at the selection problem of effective singular values in signal denoising using SVD, genetic algorithm is introduced and central difference quotient spectrum is put forward. Firstly energy calculation of effective components is adopted as the fitness function, and suitable genetic algorithm is designed for the optimization of denoising Hankel matrix. Then geometric meanings of difference quotient ways are analyzed, characteristics of the singular value curve and subtle relations between this curve and the central difference quotient way are studied. Finally central difference quotient spectrum of singular value is put forward. The results show that compared with exhaustive method, the highest energy of effective components and its optimal matrix structure can be quickly obtained with the designed genetic algorithm. Compared with the singular value curve, maximum peak position which represents the boundary of noise signals and ideal signals can be clearly shown on central difference quotient spectrum curve, and the number of effective singular values is accurately gained. On these basis, effect of signal denoising using SVD can reach to the best state.