29 April 2013 Coherent optical implementations of the fast Fourier transform and their comparison to the optical implementation of the quantum Fourier transform
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Abstract
Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar.
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Rupert C. D. Young, Philip M. Birch, Chris R. Chatwin, "Coherent optical implementations of the fast Fourier transform and their comparison to the optical implementation of the quantum Fourier transform", Proc. SPIE 8748, Optical Pattern Recognition XXIV, 874806 (29 April 2013); doi: 10.1117/12.2014042; https://doi.org/10.1117/12.2014042
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