Hartley transform

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

Type-2 computability on spaces of integrable functions

Abstract: Using Type-2 theory of effectivity, we define computability notions on the spaces of Lebesgue-integrable functions on the real line that are based on two natural approaches to integrability from measure theory. We show that Fourier transform and convolution on these spaces are computable operators with respect to these representations. By means of the orthonormal basis of Hermite functions in L2, we show the existence of a linear complexity bound for the Fourier transform. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hartley transform in compression of medical ultrasonic images

Abstract: In this paper the Hartley transform has been used for both compression and filtering of medical ultrasonic images. The Hartley transform shares some features of the Fourier transform and, most importantly, there exists a computationally effective butterfly algorithm of the transform. Compression relies on filtering out higher harmonics of the forward Hartley transform and saving the result rather as the image than the coefficients of the transform. In this case the images' size is reduced 16 times without significant loss of valuable medical information.

Fixed-point error analysis of fast Hartley transform

Abstract: Fast Hartley transform (FHT) has been proposed recently by Bracewell. This is closely related to the fast Fourier transform (FFT) However, it has two advantages over the FFT, namely, the forward and inverse transforms are the same; and the Hartley transformed outputs are real-valued, rather than complex data, Hence, the speed of computation can be increased by 50% for performing fast convolution or correlation. These properties have led to investigations to use the Hartley transform for time-efficient discrete Fourier analysis of real signals. In this paper, the error-performance of radix-2 decimation-in-time and decimation-in-frequency form of the fast Hartley transform algorithm has been studied. The analysis assumes fixed-point sign magnitude arithmetic. The analysis is carried out for decimation-in-time and decimation-in-frequency form of the fast Hartley transform algorithms, assuming all the errors to be uncorrelated. Then, the analysis is carried out, assuming the truncation errors to be correlated, in the case of decimation-in-frequency form of FHT. The predicted results are compared with computer simulation studies and those obtained in the case of fast Fourier transform. It has been observed that the expressions obtained in the analysis are similar to those obtained in the case of FFT for the corresponding cases.

The fast Hartley transform on the hypercube multiprocessors

Abstract: The Fast Hartley Transform is a promising alternative to the Fast Fourier Transform when the processed data are real numbers. The hypercube implementation of the FHT is largely dependent on the way the computation is partitioned. A partitioning algorithm is presented which generates evenly-loaded tasks on each node and demands only a regular communication topology — the Hartley graph. Mapping from the Hartley graph to the Gray graph (binary n-cube) is straightforward, since the Hartley graph has a similar structure as the Gray graph. However, the communication is not always between the nearest neighbors and thus may take some extra time. Moreover, the slowness of the communication in the presently available architectures imposes a limitation on the speedup when a large number of processors are used.