Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

A Cost-Effective and Efficient Scheme for Optical OFDM in Short-Range IM/DD Systems

Abstract: We propose a cost-effective and efficient modulation scheme for intensity-modulated and direct-detection (IM/DD) optical orthogonal frequency division multiplexing (O-OFDM) systems, which combines complex-to-real transform (C2RT) and fast Hartley transform (FHT), named as fast-fast Fourier transform (FFT). The proposed scheme can modulate the complex constellation by the real-valued operations. Compared with the FFT method, the same OFDM signal can also be generated by fast-FFT, but the computational complexity nearly halved. Meanwhile, compared with the FHT scheme, fast-FFT can modulate the complex constellations by adding a simple C2RT module for a wide applicable range. The transmission experiment of over 50-km standard single-mode fiber (SSMF) has been implemented to verify the feasibility of fast-FFT-based IM/DD O-OFDM systems, including asymmetrically clipping and DC-bias O-OFDM systems. It reveals that fast-FFT shares the same bit-error-rate (BER) performance as FFT, but fast-FFT shows superiority on computational complexity.

Short-space Fourier transform image processing

Abstract: The short-space Fourier transform (SSFT) is introduced as a means of describing discrete multi-dimensional signals of finite extent. It is an adaptation of the short-time Fourier transform developed for one-dimensional infinite-duration signals such as speech. By reflectively extending the finite signal segment, one can imagine an infinite duration signal which is "continuous." The proposed SSFT is the multidimensional generalization of the short-time Fourier transform operating upon the resulting infinite duration signal. Because boundary "discontinuities" are avoided, the proposed SSFT provides a transform representation free of extraneous spectral energy. An efficient algorithm for computing the SSET is described. SSFT image coding, an important application of the new transform method, provides localized spectral information without the undesirable phenomenon of "blocking effects."

The Discrete Hartley Transform

Abstract: This chapter introduces the DHT and discusses those aspects of its solution, as obtained via the FHT, which make it an attractive choice for applying to the real-data DFT problem. This involves first showing how the DFT may be obtained from the DHT, and vice versa, followed by a discussion of those fundamental theorems, common to both the DFT and DHT algorithms, which enable the input data sets to be similarly related to their respective transforms and thus enable the DHT to be used for solving those DSP-based problems commonly addressed via the DFT, and vice versa. The limitations of existing FHT algorithms are then discussed bearing in mind the ultimate objective of mapping any subsequent solution onto silicon-based parallel computing equipment. A discussion is finally provided relating to the results obtained in the chapter.