Programmable incoherent Newton-Cotes optical integrator

Abstract

A discrete-time integrator is a processor whose output pulse sequence is obtained by approximating the integral of a continuous-time signal from the samples of that signal. A programmable incoherent Newton-Cotes optical integrator (INCOI) is theoretically proposed. The classical numerical integration technique is employed to develop, to our knowledge, for the first time, a generalised theory of the Newton-Cotes digital integrator. Based on this developed theory, we propose algorithms and techniques for the synthesis and realisation of the programmable INCOI processor using incoherent amplified fibre-optic signal processing architectures. Several types of input pulse sequences, such as polynomials of various orders and the exponential pulse, are chosen as examples for illustration of the incoherent processing accuracy of the proposed programmable INCOI processor in the time domain. Although the analysis is directed at fibre-optic signal processors, the methodology and the results are applicable to other physical systems.