Optical Hartley-transform-based adaptive filter

Abstract

A novel optical architecture is presented that is based on the Hartley transform implementation of the classical adaptive least mean square (LMS) algorithm. The Hartley transform is employed to transform the time-domain signal of interest into the frequency domain, where filtering is performed via multiplication by the adaptively controlled filter transfer function. The inverse Hartley transform is then applied to this product resulting in the desired signal estimate, which is then subtracted from the desired signal to obtain the error to be used to upthte the filter transfer function. In addition to the presentation of this algorithm and the optical implementation, performance assessments based on the number of calculations required for the digital and optical approaches are provided.

Optical Fourier and Hartley transform adaptive filters

“…The optical generation of the Fourier transform and Hartley transform algorithms is based on a matrix-processing approach to realize the required transform and inverse transform operations [8]. Once in the frequency domain, all processing is performed optically.…”