Showing papers on "Discrete Hartley transform published in 1986"
Book•
01 Jan 1986TL;DR: The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
Abstract: The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
437 citations
01 Sep 1986
TL;DR: The fast Hartley transform algorithm as discussed by the authors offers an alternative to the fast Fourier transform, with the advantages of not requiring complex arithmetic or a sign change of i to distinguish inverse transformation from direct.
Abstract: The fast Hartley transform algorithm introduced in 1984 offers an alternative to the fast Fourier transform, with the advantages of not requiring complex arithmetic or a sign change of i to distinguish inverse transformation from direct. A two-dimensional extension is described that speeds up Fourier transformation of real digital images.
128 citations
TL;DR: A relationship between the discrete cosine transform (DCT) and the discrete Hartleytransform (DHT) is derived and it leads to a new fast and numerically stable algorithm for the DCT.
Abstract: A relationship between the discrete cosine transform (DCT) and the discrete Hartley transform (DHT) is derived. It leads to a new fast and numerically stable algorithm for the DCT.
76 citations
TL;DR: It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform, and a Chinese remainder theorem is derived for integer lattices.
Abstract: In this paper, the prime factor algorithm for the evaluation of a one-dimensional discrete Fourier transform is generalized to the evaluation of multidimensional discrete Fourier transforms defined on arbitrary periodic sampling lattices. It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform. As a sidelight to the derivation of the algorithm, a Chinese remainder theorem is derived for integer lattices.
64 citations
01 May 1986
TL;DR: A new multidimensional Hartley transform is defined and a vector-radix algorithm for fast computation of the transform is developed that is shown to be faster (in terms of multiplication and addition count) compared to other related algorithms.
Abstract: A new multidimensional Hartley transform is defined and a vector-radix algorithm for fast computation of the transform is developed. The algorithm is shown to be faster (in terms of multiplication and addition count) compared to other related algorithms.
41 citations
TL;DR: The split radix was used to develop a fast Hartley transform algorithm, it is performed ''in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms'' as discussed by the authors.
Abstract: The split radix is used to develop a fast Hartley transform algorithm, it is performed `in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms.
40 citations
TL;DR: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versions, and the FHT can transform one real array of length N in half the time that it takes the FFT to process a complex array.
Abstract: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versionsAny FFT can thus be converted, by a few indexing changes, into a Fast Hartley Transform which is equally efficient, in terms of floating point operations per real datum transformed The FHT can therefore transform one real array of length N in half the time that it takes the FFT to process a complex array of length N Several tricks to speed up both FHT and FFT are presented and a Fortran version of the FHT is supplied which delivers the result in $75\log _2 N$ multiplications and $175\log _2 N$ additions
37 citations
TL;DR: In this article, it was shown that the most natural extension of the DHT to two dimensions fails to be separate in two dimensions, and is therefore inefficient, and an alternative separable form is considered, corresponding convolution theorem is derived.
Abstract: Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
35 citations
01 Jan 1986
TL;DR: Fast algorithms for computation of the discrete cosine transform (DCT) are evaluated through the fast Fourier transform and also by the direct method.
Abstract: Fast algorithms for computation of the discrete cosine transform (DCT) are evaluated. Implementation via the fast Fourier transform and also by the direct method are considered. DCT algorithms for arbitrary sequence lengths are also included.
21 citations
14 citations
TL;DR: New techniques which are especially efficient for 2- and 3-dimensional DFT implemented on a Cray X-MP are presented and compared to existing techniques.
01 Jan 1986
TL;DR: Ideal methods for shrinking or expanding a discrete sequence, image, or image sequence are described and fast implementations that make use of the discrete Fourier transform or the discrete Hartley transform lead to a new multiresolution image pyramid.
Abstract: Ideal methods are described for shrinking or expanding a discrete sequence, image, or image sequence. The methods are ideal in the sense that they preserve the frequency spectrum of the input up to the Nyquist limit of the input or output, whichever is smaller. Fast implementations that make use of the discrete Fourier transform or the discrete Hartley transform are described. The techniques lead to a new multiresolution image pyramid.
TL;DR: A new hybrid optical/digital processor that computes the geometric moments using the recently introduced Hartley transform (HT), which has the attractive property of being real when the signal is real.
Abstract: Geometric moments are useful in pattern recognition, and several optical methods have been proposed for their calculation. In this paper, we present a new hybrid optical/digital processor that computes the geometric moments using the recently introduced Hartley transform (HT). This transform has the attractive property of being real when the signal is real. We prove an important result, that all geometric moments of an image can be computed recursively from the various partial derivatives (near origin) of the HT intensity. An analytical example is provided to illustrate the proposed method.
01 Jan 1986
TL;DR: A paired tensor representation of each component Fp,s of the spectrum of the signal in the form of the corresponding N/2-dimensional vector F̄ ′ p,s the paired vector representation is called.
Abstract: Since for each t ∈ [1, N/2], we have W t+N/2 = −W , one can also represent component (1) at the point (p, s) by the corresponding N/2-dimensional vector F̄ ′ p,s = (f ′ p,s,1, f ′ p,s,2, ..., f ′ p,s,N/2), whose components are calculated from the components of the corresponding initial vector F̄p,s by formula f ′ p,s,t = fp,s,t − fp,s,t+N/2, t = 1 ÷ N/2. (5) We call such representation of each component Fp,s of the spectrum in the form of the corresponding N/2-dimensional vector F̄ ′ p,s the paired vector representation, to distinct it from the original vector representation F̄p,s, and the constructed tensor of the 3rd order (f ′ p,s,t; p, s, = 1 ÷ N, t = 1 ÷ N/2 to be the paired tensor of the Fourier-spectrum. As for the original tensor representation of the spectrum of the signal, when for any p, s and k the following formula was valid [1]
CNET1
TL;DR: Two approaches using Fourier or Hartley transforms are first compared, showing that the recently proposed FFT algorithms for real data present a lower arithmetic complexity than the corresponding DHT-based approach.
Abstract: Recently, new fast transforms (such as the discrete Hartley transform in particular) have been proposed which are best suited for the computation of cyclic convolution of real sequences. Two approaches using Fourier or Hartley transforms are first compared, showing that the recently proposed FFT algorithms for real data present a lower arithmetic complexity than the corresponding DHT-based approach. Improvements are made to both types of algorithms, leading to different trade offs between arithmetic and structural complexity. We also present a new Hartley Transform algorithm with lower arithmetic complexity than any previously published one.
TL;DR: In this paper, the discrete frequency Fourier transform (DFFT) is shown to be a useful transform in its own right for spatial domain image reconstruction, filling a gap in the theory and aids the designer in understanding problems which have inherently sampled frequency domains.
Abstract: In certain signal processing applications it may be required to reconstruct a spatial domain image form samples of its Fourier transform. For problems such as this it may be useful to use the dual of the well-known discrete time Fourier transform (DTFT) for purposes of analysis and design. In this paper, this dual concept, called the discrete frequency Fourier transform (DFFT), is shown to be a useful transform in its own right. In addition to being useful for certain physical problems, the DFFT fills a gap in the theory and aids the designer in understanding problems which have inherently sampled frequency domains.
01 Apr 1986
TL;DR: A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms and a new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm.
Abstract: A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms. A new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm. A new fast algorithm for real-data DFT based on a new algorithm for the discrete Hartley transform is also proposed.
TL;DR: The present paper relies on the conjugate property of the generalized DFT in order to define novel, advantageous algorithms for the in-place calculation of the DFT of multidimensional sequences.
Abstract: The computation of the discrete Fourier transform (DFT) of real multidimensional sequences requires an extraordinary amount of computer memory. The in-place calculation of the discrete Fourier transform reduces the required memory and is thus highly desirable. The present paper relies on the conjugate property of the generalized DFT in order to define novel, advantageous algorithms for the in-place calculation of the DFT of multidimensional sequences.
TL;DR: Primary goal of this work is application of self-reconfiguration Algorithms to Fourier Transform architectures, as required for installation of the processing system on satellites.
01 Apr 1986
TL;DR: The effect of using ideal filter transfer function in transform domain decimation on the quality of the decimated images is investigated and the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.
Abstract: Decimation is normally carried out in two passes; lowpass filtering and subsampling where the latter is normally performed in the time domain. This paper describes a technique whereby both the operations can be combined in the transform domain. The two-dimensional decimation scheme is first implemented in the discrete Fourier transform domain and then extended to the discrete cosine transform domain. It is further applied to a non-sinusoidal i.e. Hadamard transform domain. The effect of using ideal filter transfer function in transform domain decimation on the quality of the decimated images is investigated. This approach results in greater computational efficiency as the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.
01 Apr 1986
TL;DR: Criteria for measuring the closeness of a transform to the Karhunen-Loeve transform show that the phase shift cosine transform measures closer to the even part of the KLT than the version II of the discrete Cosine transform (DCT-II).
Abstract: A new transform, the phase shift cosine transform (PSCT), is introduced. It almost diagonizes the even part of the covariance matrix of a high correlated Markov-I sequence. Several criteria are established for measuring the closeness of a transform to the Karhunen-Loeve transform (KLT). All these criteria show that the PSCT measures closer to the even part of the KLT than the version II of the discrete cosine transform (DCT-II).
TL;DR: The performance of the COSHAD transform is investigated in terms of some standard quantitative performance measures such as variance distribution, Wiener filtering, decorrelation property and transform image coding, and its utility and effectiveness are compared with those of other discrete transforms.
24 Sep 1986
TL;DR: In this article, the Hartley transform (HT) is used to compute the geometric moments of an image, which can be computed recursively from the various partial derivatives (near origin) of the HT intensity.
Abstract: In this paper, we present a new hybrid optical / digital processor that computes the geometric moments using the recently introduced Hartley transform (HT) . This transform has the attractive property of being real when the signal is real. We prove an important result that all geometric moments of an image can be computed recursively from the various partial derivatives (near origin) of the HT intensity .
Dissertation•
01 Jan 1986
17 Sep 1986
TL;DR: It is shown, that the Shuffle/Exchange-Network (S/E) is optimal for this purpose in a quite general sense.
Abstract: It is known, that the Shuffle/Exchange-Network (S/E) is well suited to perform the parallel Fast Fourier Transform (FFT). In this paper we show, that it is optimal for this purpose in a quite general sense:
15 Oct 1986
TL;DR: A unified analysis of a class of unitary transforms including the discrete Fourier, the Walsh Hadamard, the discrete Hartley, and the discrete cosine transforms, which leads to a fast, efficient recursive algorithm for the discreteHartley transform.
Abstract: This paper presents a unified analysis of a class of unitary transforms including the discrete Fourier, the Walsh Hadamard, the discrete Hartley, and the discrete cosine transforms. These transforms possess a common recursive property that allows us to obtain the next higher-order transform from two identical, preceding lower-order transforms. This recursive property eventually leads us to formulate a fast, efficient recursive algorithm for the discrete Hartley transform, from which the fast processing algorithm for the discrete cosine transform can also be obtained. Hybrid implementations using state-of-the-art integrated optics in digital format have also been proposed for such fast, efficient processing algorithms.