Hartley transform

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

Basefield transforms with the convolution property

Abstract: We present a general framework for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over the reals, but is shown to be valid over more general fields. We show that these basefield transforms can be viewed as "projections" of the discrete Fourier transform (DFT). Furthermore, by imposing an additional condition on the projections, one may obtain self-inverse versions of the basefield transforms. Applying the theory to the real and complex fields, we show that the projection of the complex DFT results in the discrete combinational Fourier transform (DCFT) and that the imposition of the self-inverse condition on the DCFT yields the discrete Hartley transform (DHT). Additionally, we show that the method of projection may be used to derive efficient basefield transform algorithms by projecting standard FFT algorithms from the extension field to the basefield. Using such an approach, we show that many of the existing real Hartley algorithms are projections of well-known FFT algorithms. >

Recursive formulation of short-time discrete trigonometric transforms

Abstract: Recursive formulations of the moving-window discrete Fourier transform (DFT) are well known. However, recursive versions of other useful discrete transforms, like the moving-window discrete cosine transform (DCT), discrete sine transform (DST), or discrete Hartley transform (DHT), have not been developed so far. In this paper, second-order recursive expressions for the DCT, DST, and DHT, intended for real-valued windowed sequences, are presented.

Inversion of the circular averages transform using the Funk transform

Abstract: The integral of a function defined on the half-plane along the semi-circles centered on the boundary of the half-plane is known as the circular averages transform. Circular averages transform arises in many tomographic image reconstruction problems. In particular, in synthetic aperture radar (SAR) when the transmitting and receiving antennas are colocated, the received signal is modeled as the integral of the ground reflectivity function of the illuminated scene over the intersection of spheres centered at the antenna location and the surface topography. When the surface topography is flat the received signal becomes the circular averages transform of the ground reflectivity function. Thus, SAR image formation requires inversion of the circular averages transform. Apart from SAR, circular averages transform also arises in thermo-acoustic tomography and sonar inverse problems. In this paper, we present a new inversion method for the circular averages transform using the Funk transform. For a function defined on the unit sphere, its Funk transform is given by the integrals of the function along the great circles. We used hyperbolic geometry to establish a diffeomorphism between the circular averages transform, hyperbolic x-ray and Funk transforms. The method is exact and numerically efficient when fast Fourier transforms over the sphere are used. We present numerical simulations to demonstrate the performance of the inversion method.Dedicated to Dennis Healy, a friend of Applied Mathematics and Engineering.

Constant envelope coherent optical OFDM based on fast Hartley transform

Abstract: In this paper the authors discuss the feasibility of a constant envelope optical OFDM based on fast Hartley transform. The digital signal processing output drives an optical phase modulator for obtaining a 0 dB PAPR signal at the transmission side, whereas the use of a Hartley transform increases power efficiency and relaxes the level of the constellation used. Additionally, a set of simulations of the system are presented, showing a back-to-back sensitivity of −34.6 dBm for a 10−3 BER.