High speed spectral estimation using an optical implementation of the discrete Hartley transform

An efficient method for optically obtaining the modulus of the discrete Fourier transform (DFT) of a real input is presented. The method involves performing the discrete Hartley transform (DHT) by way of a simple vector-matrix multiplication with an incoherent optical processor. The DFT is directly obtainable from the DHT and vice-versa. However, the Hartley transform of a real function is real. The kernel of the Hartley transform is real, which makes it more suitable for application in an incoherent optical processor than the complex Fourier kernel. High-speed spectral estimation of sinusoidal radar for electronic warfare purposes is a potential application. Experimental results that demonstrate the method are presented.<>