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We present a novel optical orthogonal frequency division multiplexing (O-OFDM) scheme, suitable for intensity-modulated direct-detection systems, where the modulation/demodulation processing takes advantage of the fast Hartley transform algorithm. Due to the properties of the discrete Hartley transform (DHT), the conventional transmission scheme can be streamlined. We demonstrate that asymmetrically clipping (AC) technique can also be applied to DHT-based OFDM; the signal can be transmitted without the need of a DC bias, resulting in a power-efficient system, not affected by clipping noise. Hermitian symmetry is not required for the input signal. Therefore, this technique supports the double of input symbols compared to both AC and DC-biased O-OFDM, based on standard Fourier processing. The analysis in an additive white Gaussian noise channel shows that the same performance can be achieved by replacing 4, 16, and 64 QAM (quadrature-amplitude modulation) AC optical-OFDM with a simpler system based on DHT, using binary phase-shift keying (BPSK), 4 and 8 PAM (pulse-amplitude modulation), respectively.