Theory of a FIR optical digital differentiator

Abstract

An optical realization of a proposed family of the finite impulse response (FIR) qth-order mth-derivative digital differentiators (under coherent operation), whose transfer functions are derived from the well-known numerical differentiation scheme (namely, the backward Taylor series expansion), using the amplified fiber optic transversal filters is presented. Several input pulse shapes, such as polynomials of various orders and the Gaussian and exponential pulses, are chosen as examples for illustration of the accuracy of the proposed optically realized differentiators. A mathematical model describing the dynamic (or transient) response of any optical discrete-time systems using the z-transform technique is proposed. The real-time performances of the proposed differentiators have been analyzed using both the steady-state and the dynamic analyses, Although the analysis is directed at fiber optic systems, the methodology and the results are applicable to other physical systems.