An INverse COnvolution MEthod for wavenumber extraction (INCOME): Formulations and applications

Abstract

This paper deals with the extraction of wave features in elastic media. An inverse approach is proposed for the identification of wave dispersion characteristics (e.g. k-space) in one- and two-dimensional structures (1D, 2D). The proposed method is similar to the ESPRIT algorithm and the Prony series method and can be considered as an extension of the latter, specifically when applied to 1D problems. By using a convolution framework, the method is extended to the 2D case for which it allows the estimation of the full k-space by solving a linear problem. The method is called INverse COnvolution MEthod (INCOME). The formulation of INCOME is first detailed and mathematically justified. Both the 1D and 2D cases are detailed and explained. Then several examples are presented for assessing the validity domain of INCOME. These numerical tests clearly show the relevance of INCOME for structured inputs with periodic characteristics.