Abstract

This paper presents a generalization of the discrete $z$ transform algorithm. It is shown that the GOD-ZT algorithm is a generalization of several important conventional discrete transforms. Based on the GOD-ZT algorithm, a tunable general optical discrete $z$ transform (GOD-ZT) processor is synthesized using the silica-based finite impulse response transversal filter. To demonstrate the effectiveness of the method, the design and simulation of a tunable optical discrete Fourier transform (ODFT) processor as a special case of the synthesized GOD-ZT processor is presented. It is also shown that the ODFT processor can function as a real-time optical spectrum analyzer. The tunable ODFT has an important potential application as a tunable optical demultiplexer at the receiver end of an optical orthogonal frequency-division multiplexing transmission system.

© 2016 Optical Society of America

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