Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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06 May 2001
TL;DR: The author derives a new algorithm that can formulate the 1-D DHT into cyclic convolution, and realizes it in a DA-based array that utilizes identical ROM modules, and eliminates the accumulation loop in the processing elements (PE's).
Abstract: This paper presents a new distributed arithmetic (DA) based array for the (1-D) any-length discrete Hartley transform (DHT). The author derives a new algorithm that can formulate the 1-D DHT into cyclic convolution, and realizes it in a DA-based array that utilizes identical ROM modules, and eliminates the accumulation loop in the processing elements (PE's). The proposed approach can be applied to other transforms like DFT, DCT and DST.
9 citations
Proceedings Article•
01 Jan 2000TL;DR: An easily comprehensible and efficient implementation of the fast HT and its multi-dimensional extension is demonstrated by adapting this algorithm to volume rendering by the projection-slice theorem and by the use for filter analysis in frequency domain to demonstrate the importance of the HT in this application area.
Abstract: The Fast Hartley Transform (FHT), a discrete version of the Hartley Transform (HT), has been studied in various papers and shown to be faster and more convenient to implement and handle than the corresponding Fast Fourier Transform (FFT). As the HT is not as nicely separable as the FT, a multidimensional version of the HT needs to perform a final correction step to convert the result of separate HTs for each dimension into the final multi-dimensional transform. Although there exist algorithms for two and three dimensions, no generalization to arbitrary dimensions can be found in the literature. We demonstrate an easily comprehensible and efficient implementation of the fast HT and its multi-dimensional extension. By adapting this algorithm to volume rendering by the projection-slice theorem and by the use for filter analysis in frequency domain we further demonstrate the importance of the HT in this application area.
9 citations
01 Jan 2001
TL;DR: An approximate fast Hartley transform (FHT) based method to compute the discrete Fourier transform (DFT) coefficients approximately is proposed and it is found that the proposed method is computationally superior to both the radix 2 fast Fouriers transform (FFT) and also the radIX 2 approximate FFT algorithms.
Abstract: We propose an approximate fast Hartley transform (FHT) based method to compute the discrete Fourier transform (DFT) coefficients approximately. The approximate FHT is implemented using a periodic discrete wavelet transform (DWT). We find that the proposed method is computationally superior to both the radix 2 fast Fourier transform (FFT) and also the radix 2 approximate FFT algorithms.
9 citations
9 citations
IBM1
TL;DR: The sinc and cosinc transform (SCT) as mentioned in this paper uses Walsh functions to obtain the Fourier transform, which converts a staircase approximation of a function to a set of sinc terms in the frequency domain.
Abstract: A new transform, the sinc and cosinc transform, uses Walsh functions to obtain the Fourier transform. This technique converts a staircase approximation of a function to a set of sinc and cosinc terms in the frequency domain that is equivalent to the Fourier transform. The calculation is slower than the fast Fourier transform (FFT) but is devoid of aliasing. The interpolation and scaling in the frequency domain are built in, and any frequency point may be chosen without changing the number or spacing of the samples in the time domain. The intervening set of coefficients is computed more rapidly than those obtained using the fast Hadamard transform.
9 citations