Topic
Discrete Hartley transform
About: Discrete Hartley transform is a research topic. Over the lifetime, 2043 publications have been published within this topic receiving 58835 citations.
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TL;DR: A new implementation of the real-valued split-radix FFT is presented, an algorithm that uses fewer operations than any otherreal-valued power-of-2-length FFT.
Abstract: This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses fewer operations than any other real-valued power-of-2-length FFT. We also compare the performance of inherently real-valued transform algorithms such as the fast Hartley transform (FHT) and the fast cosine transform (FCT) to real-valued FFT algorithms for the computation of power spectra and cyclic convolutions. Comparisons of these techniques reveal that the alternative techniques always require more additions than a method based on a real-valued FFT algorithm and result in computer code of equal or greater length and complexity.
489 citations
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TL;DR: In this paper, a computationally efficient numerical procedure to generate 2D correlation spectra from a set of spectral data collected at certain discrete intervals of an external physical variable, such as time, temperature, pressure, etc., is proposed.
Abstract: A computationally efficient numerical procedure to generate twodimensional (2D) correlation spectra from a set of spectral data collected at certain discrete intervals of an external physical variable, such as time, temperature, pressure, etc., is proposed. The method is based on the use of a discrete Hilbert transform algorithm which carries out the time-domain orthogonal transformation of dynamic spectra. The direct computation of a discrete Hilbert transform provides a definite computational advantage over the more traditional fast Fourier transform route, as long as the total number of discrete spectral data traces does not significantly exceed 40. Furthermore, the mathematical equivalence between the Hilbert transform approach and the original formal definition based on the Fourier transform offers an additional useful insight into the true nature of the asynchronous 2D spectrum, which may be regarded as a time-domain cross-correlation function between orthogonally transformed dynamic spectral intensity variations.
473 citations
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TL;DR: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable and promises to speed up Fourier-transform calculations.
Abstract: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable. The inverse DHT is identical with the direct transform, and so it is not necessary to keep track of the +i and −i versions as with the DFT. Also, the DHT has real rather than complex values and thus does not require provision for complex arithmetic or separately managed storage for real and imaginary parts. Nevertheless, the DFT is directly obtainable from the DHT by a simple additive operation. In most image-processing applications the convolution of two data sequences f1 and f2 is given by DHT of [(DHT of f1) × (DHT of f2)], which is a rather simpler algorithm than the DFT permits, especially if images are. to be manipulated in two dimensions. It permits faster computing. Since the speed of the fast Fourier transform depends on the number of multiplications, and since one complex multiplication equals four real multiplications, a fast Hartley transform also promises to speed up Fourier-transform calculations. The name discrete Hartley transform is proposed because the DHT bears the same relation to an integral transform described by Hartley [ HartleyR. V. L., Proc. IRE30, 144 ( 1942)] as the DFT bears to the Fourier transform.
465 citations
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01 Aug 1984TL;DR: The Fast Hartley Transform (FHT) is as fast as or faster than the Fast Fourier Transform (FFT) and serves for all the uses such as spectral analysis, digital processing, and convolution to which the FFT is at present applied.
Abstract: A fast algorithm has been worked out for performing the Discrete Hartley Transform (DHT) of a data sequence of N elements in a time proportional to Nlog 2 N. The Fast Hartley Transform (FHT) is as fast as or faster than the Fast Fourier Transform (FFT) and serves for all the uses such as spectral analysis, digital processing, and convolution to which the FFT is at present applied. A new timing diagram (stripe diagram) is presented to illustrate the overall dependence of running time on the subroutines composing one implementation; this mode of presentation supplements the simple counting of multiplies and adds. One may view the Fast Hartley procedure as a sequence of matrix operations on the data and thus as constituting a new factorization of the DFT matrix operator; this factorization is presented. The FHT computes convolutions and power spectra distinctly faster than the FFT.
455 citations
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TL;DR: In this article, the concept of transform domain adaptive filtering is introduced and the relationship between several existing frequency-domain adaptive filtering algorithms is established, and applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filter algorithms in the areas of speech processing and adaptive line enhancers are discussed.
Abstract: The concept of transform domain adaptive filtering is introduced. In certain applications, filtering in the transform domain results in great improvements in convergence rate over the conventional time-domain adaptive filtering. The relationship between several existing frequency domain adaptive filtering algorithms is established. Applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed.
447 citations