THEORY OF A FIR OPTICAL DIGITAL DIFFERENTIATOR

An optical realization of a proposed family of the finite impulse resp onse (FIR) qth-order mth-derivative digital differentiators (under coh erent operation), whose transfer functions are derived from the well-k nown numerical differentiation scheme (namely, the backward Taylor ser ies 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 example s for illustration of the accuracy of the proposed optically realized differentiators. A mathematical model describing the dynamic (or trans ient) response of any optical discrete-time systems using the z-transf orm technique is proposed The real-time performances of the proposed d ifferentiators have been analyzed using bath the steady-state and the dynamic analyses. Although the analysis is directed at fiber optic sys tems, the methodology and the results are applicable to other physical systems.