## Abstract

An incoherent optical data-processing method is described, which has the potential for performing discrete Fourier transforms of short length at rates far exceeding those afforded by both special-purpose digital hardware and representative coherent optical processors.

© 1978 Optical Society of America

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### Equations (3)

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(1)
$$\mathbf{g}=\mathcal{H}\mathbf{f}.$$
(2)
$$\begin{array}{l}\mathbf{f}={\mathbf{f}}^{(0)}+{\mathbf{f}}^{(1)}\hspace{0.17em}\text{exp}(j2\pi /3)+{\mathbf{f}}^{(2)}\hspace{0.17em}\text{exp}(j4\pi /3),\\ \mathcal{H}={\mathcal{H}}^{(0)}+{\mathcal{H}}^{(1)}\hspace{0.17em}\text{exp}(j2\pi /3)+{\mathcal{H}}^{(2)}\hspace{0.17em}\text{exp}(j4\pi /3),\end{array}$$
(3)
$$\left[\begin{array}{l}{\mathbf{g}}^{(0)}\hfill \\ {\mathbf{g}}^{(1)}\hfill \\ {\mathbf{g}}^{(2)}\hfill \end{array}\right]=\left[\begin{array}{lll}{\mathcal{H}}^{(0)}\hfill & {\mathcal{H}}^{(2)}\hfill & {\mathcal{H}}^{(1)}\hfill \\ {\mathcal{H}}^{(1)}\hfill & {\mathcal{H}}^{(0)}\hfill & {\mathcal{H}}^{(2)}\hfill \\ {\mathcal{H}}^{(2)}\hfill & {\mathcal{H}}^{(1)}\hfill & {\mathcal{H}}^{(0)}\hfill \end{array}\right]\hspace{0.17em}\left[\begin{array}{l}{\mathbf{f}}^{(0)}\hfill \\ {\mathbf{f}}^{(1)}\hfill \\ {\mathbf{f}}^{(2)}\hfill \end{array}\right].$$