Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This paper studies some of the practical limits introduced by using a converging spherical lens of finite aperture to produce the illuminating field in the implementation of the SOFT and shows that the worst-case errors in the resulting SOFT can be quantified and avoided.
12 citations
TL;DR: A generalized running discrete transform with respect to arbitrary transform bases is introduced, and the generalized transform to the running discrete Fourier z and short-time discrete Fouriers transforms is related.
Abstract: This paper introduces a generalized running discrete transform with respect to arbitrary transform bases, and relates the generalized transform to the running discrete Fourier z and short-time discrete Fourier transforms. Concepts associated with the running and short-time discrete Fourier transforms such as 1) filter bank implementation, 2) synthesis of the original sequence by summation of the filter bank outputs, 3) frequency sampling, and 4) recursive implementations are all extended to the generalized transform case. A formula is obtained for computing the transform coefficients of a segment of data at time n recursively from the transform coefficients of the segment of data at time n - 1. The computational efficiency of this formula is studied, and the class of transforms requiring the minimum possible number of arithmetic operations per coefficient is described.
12 citations
TL;DR: In this paper, it was shown that for continuous functions, the Hilbert transform and Cauchy transform have a similar divergence behavior as for absolute integrable functions, and that for each set of the set E with Lebesgue measure zero, there exists a continuous function such that the Hilbert transformation and the cauchy transformation of this function are infinite for all points in E.
Abstract: In this paper we investigate the behavior of the Hilbert transform and the Cauchy transform. It is well known, that for absolut integrable functions the Hilbert transform and the Cauchy transform is finite almost everywhere. In this paper it is shown, that for each set \( E\subset [-\pi ,\pi ) \) with Lebesgue measure zero there exists a continuous function such that the Hilbert transform and the Cauchy transform of this function is infinite for all points of the set E. So for continuous functions the Hilbert transform and the Cauchy transform have a similar divergence behavior as for absolute integrable functions.
12 citations
24 Aug 2009
TL;DR: Four efficient block-based transceivers exploiting the displacement structure approach are proposed, which require only half the number of symbols of redundancy in comparison to the standard OFDM and SC-FD systems.
Abstract: Four efficient block-based transceivers exploiting the displacement structure approach are proposed. In terms of computational burden, the resulting systems are asymptotically as simple as orthogonal frequency-division multiplex (OFDM) and single-carrier with frequency-domain (SC-FD) equalization transceivers. Even though the effective channel impulse response must be symmetric, the novel schemes are appealing since they only use discrete Hartley transforms (DHTs) and diagonal matrices in their structures, which results in numerically efficient algorithms for the equalization process. The key feature of the proposed transceivers is their higher throughput, since they require only half the number of symbols of redundancy in comparison to the standard OFDM and SC-FD systems.
12 citations
TL;DR: A fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT) is established and alternative proof of the well-known properties of the Q wigner-Ville distribution such as inversion formula and Moyal formula is provided.
Abstract: The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT.
12 citations