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Discrete Hartley transform

About: Discrete Hartley transform is a(n) research topic. Over the lifetime, 2043 publication(s) have been published within this topic receiving 58835 citation(s). more

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01 Jan 1965-
Abstract: 1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and Linearity 10 Sampling and Series 11 The Discrete Fourier Transform and the FFT 12 The Discrete Hartley Transform 13 Relatives of the Fourier Transform 14 The Laplace Transform 15 Antennas and Optics 16 Applications in Statistics 17 Random Waveforms and Noise 18 Heat Conduction and Diffusion 19 Dynamic Power Spectra 20 Tables of sinc x, sinc2x, and exp(-71x2) 21 Solutions to Selected Problems 22 Pictorial Dictionary of Fourier Transforms 23 The Life of Joseph Fourier more

5,709 citations

Journal ArticleDOI
N. U. Ahmed1, T. Natarajan1, K. R. RaoInstitutions (1)
Abstract: A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loeve transform, which is known to be optimal. The performances of the Karhunen-Loeve and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion. more

4,205 citations

Book ChapterDOI
13 Oct 1993-
TL;DR: An indexing method for time sequences for processing similarity queries using R * -trees to index the sequences and efficiently answer similarity queries and provides experimental results which show that the method is superior to search based on sequential scanning. more

Abstract: We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences. more

2,041 citations


15 Aug 1990-
TL;DR: This paper presents two Dimensional DCT Algorithms and their relations to the Karhunen-Loeve Transform, and some applications of the DCT, which demonstrate the ability of these algorithms to solve the discrete cosine transform problem. more

Abstract: Discrete Cosine Transform. Definitions and General Properties. DCT and Its Relations to the Karhunen-Loeve Transform. Fast Algorithms for DCT-II. Two Dimensional DCT Algorithms. Performance of the DCT. Applications of the DCT. Appendices. References. Index. more

1,998 citations

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Topic's top 5 most impactful authors

Soo-Chang Pei

40 papers, 1.2K citations

Guoan Bi

14 papers, 194 citations

Ronald N. Bracewell

11 papers, 10.4K citations

Said Boussakta

10 papers, 98 citations

H. M. de Oliveira

10 papers, 45 citations