Fast optical signal filtering by means of amplitude and phase operators

Abstract

Abstract The article is devoted to a new numerical method of fast optical signal filtering. It is a unique mathematical apparatus of amplitude and phase operators, which has no analogues among the classical methods. The main advantages of the method for optical signal processing are computational simplicity, the versatility of the approach for solving various kinds of problems, and the availability of a geometric and physical interpretation of transformations. The amplitude and phase transformation algorithm, as well as its modifications, are presented in the article. It is shown that the method can be applied both to analog signals and to discrete measurements of a certain signal. The generalization of the operator to the two-dimensional case allows it to be applied to the processing of signals given on a rectangular grid. Proposed algorithm allows to achieve a significant acceleration during solving the problem of signal filtering compared with traditional fast Fourier transform.