Showing papers on "Discrete sine transform published in 1977"
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TL;DR: A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional DiscreteCosine Transform algorithms using the Fast Fourier Transform.
Abstract: A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional Discrete Cosine Transform algorithms using the Fast Fourier Transform. The algorithm is derived in the form of matrices and illustrated by a signal-flow graph, which may be readily translated to hardware or software implementations.
1,301 citations
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IBM1
TL;DR: A new approach to the computation of the discrete Fourier transform (DFT) with significantly reduced number of multiplication operations; it does not increase the number of addition operations in many cases.
Abstract: Recently, Dr. Shmuel Winograd discovered a new approach to the computation of the discrete Fourier transform (DFT). Relative to fast Fourier transform (FFT), the Winograd Fourier transform algorithm (WFTA) significantly reduces the number of multiplication operations; it does not increase the number of addition operations in many cases. This paper introduces the new algorithm and discusses the operations comparison problem. A guide for programming is included, as are some preliminary running times.
178 citations
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102 citations
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IBM1
TL;DR: In this paper, a method for determining the initial values of the coefficients of a transversal equalizer in a data transmission system in which the transmission channel creates frequency shift is presented.
Abstract: A method of and apparatus for determining during an initial training period the initial values of the coefficients of a transversal equalizer in a data transmission system in which the transmission channel creates frequency shift. The received periodic training sequence is modulated by a time-domain window signal whose Fourier transform exhibits a relatively flat central peak and has comparatively low values in the vicinity of those frequencies which are a multiple of the inverse of the period of the transmitted sequence, and the discrete Fourier transform Wk of the modulated signal is computed. The values of the coefficients of the equalizer are obtained by computing the inverse discrete Fourier transform of the ratio Fk =Zk /Wk, where Zk is the discrete Fourier transform of the transmitted sequence.
58 citations
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TL;DR: The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT and is used to filter a two-dimensional picture, and the results are presented with a comparison to the standard FFT.
Abstract: A transform analogous to the discrete Fourier transform is defined on the Galois field GF(p), where p is a prime of the form k X 2n + 1, where k and n are integers. Such transforms offer a substantial variety of possible transform lengths and dynamic ranges. The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT. A transform of this type is used to filter a two-dimensional picture (e.g., 256 X 256 samples), and the results are presented with a comparison to the standard FFT. An absence of roundoff errors is an important feature of this technique.
44 citations
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TL;DR: In this article, the Fourier transform of the gravity field due to a finite dipping dike is derived and its real and imaginary components are separated and simple relations that can be used to estimate the unknown parameters of the dike.
Abstract: The Fourier transform of the gravity field due to a finite dipping dike is derived and its real and imaginary components are separated. Analysis of these two functions in a certain high-frequency range yields simple relations that can be used to estimate the unknown parameters of the dike. The theoretical considerations are tested on synthetic data after performing the discrete Fourier transform (DFT), and the validity of the method of interpretation is established from a comparison of the actual and estimated parameters.
24 citations
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TL;DR: In this article, a discrete filtering technique based on circular convolution is presented, which is shown to compare favorably with DFT and FFT filtering, in terms of error accumulation.
Abstract: A discrete filtering technique based on circular convolution is presented. The discrete Hilbert transform (DHT), in matrix form and other matrices for filtering by circular convolution, is shown to compare favorably with DFT and FFT filtering. The comparison is presented in terms of error accumulation.
19 citations
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TL;DR: In this paper, the gravity effect of an infinite horizontal trapezoidal prism is derived and its Fourier spectrum is analyzed so as to yield information about four parameters of the causative structure, namely the depths to the upper and lower surfaces, width of the upper surface, and the inclination of the sides.
Abstract: The gravity effect of an infinite horizontal trapezoidal prism is derived and its Fourier spectrum is analyzed so as to yield information about four parameters of the causative structure, namely the depths to the upper and lower surfaces, width of the upper surface, and the inclination of the sides. In order to test the applicability of the method, synthetic data are constructed by digitizing the theoretical gravity effect. Subsequently, the corresponding Discrete Fourier Transform (DFT) is obtained. The parameters evaluated from the DFT are observed to be sufficiently close to the chosen values.
16 citations
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01 May 1977TL;DR: This new algorithm is designed to remove the requirement for transposition, thereby, greatly increasing the speed of the process, which is extremely valuable on small disc based computers.
Abstract: Conventional two dimensional fast Fourier transforms become very slow if the size of the matrix becomes too large to be contained in memory. This is due to the transposition of the matrix that is required. This new algorithm is designed to remove the requirement for transposition, thereby, greatly increasing the speed of the process. This algorithm is extremely valuable on small disc based computers.
14 citations
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TL;DR: In this article, a distribution network provides signals that are representative of the sum of the amplitudes of values of the first, second and third terms of a Fourier cosine series expansion of the discrete inverse Fourier transform of a desired pattern of excitation of a purality of radiators.
Abstract: A distribution network provides signals that are representative of the sum of the amplitudes of values of the first, second and third terms of a Fourier cosine series expansion of the discrete inverse Fourier transform of a desired pattern of excitation of a purality of radiators. The signals are coupled to an orthogonal beam matrix via a plurality of phase shifters to provide a signal representation of an approximation of the inverse transform. The matrix is connected to the radiators whereby the desired pattern of excitation is applied to the radiators.
12 citations
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TL;DR: It is found that the rewriting of the Fourier transform to scale data only when arithmetic overflow occurs, rather than before each pass, results in a twofold increase in the available dynamic range.
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18 Mar 1977TL;DR: In this paper, a series of stored images representing sine and cosine components of the Fourier transform is generated to obtain a fast, two-dimensional transform of the image.
Abstract: Two dimensional optical or electrical images are processed through a storage tube designed to yield the correlation function between the input images and stored images. By generating a series of stored images representing sine and cosine components of the Fourier transform, a fast, two-dimensional transform of the image is obtained.
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TL;DR: In this paper, the orthogonality conditions that must be fulfilled by the transform factor α of a NTFT of length N, are proven based upon the possibility of cancelling all nonzero factors of the form (αq-1), q = 1, 2,..., N - 1.
Abstract: The proof of the orthogonality conditions that must be fulfilled by the transform factor α of a NTFT of length N, is based upon the possibility of cancelling all nonzero factors of the form (αq- 1), q = 1, 2,..., N - 1. In a residue ring containing zero divisors, this is not allowed, unless all such factors can be shown not to be divisors of zero. It is shown that this is the case, when a is any primitive Nth root of unity, N being an allowed transform legnth. At the same time, a property is established that helps to reduce the amount of searching needed to find suitable transform factors.
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TL;DR: A classification of methods for generating discrete Fourier transform pairs is given, followed by a table of 29 pairs that shows hundreds of additional nonobvious finite identities can be deduced by using the Rayleigh-Parseval formula and convolutions.
Abstract: A classification of methods for generating discrete Fourier transform pairs is given, followed by a table of 29 pairs. Many of these are new, whereas some have been collected from various literature sources. We have tried to make the table interesting rather than comprehensive. The generalization of the Gaussian sums is a good example. Hundreds of additional nonobvious finite identities can be deduced by using the Rayleigh-Parseval formula and convolutions.
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TL;DR: This work shows how to perform a number-theoretic transform (n.t.t.) using an algorithm analogous to that of S.s. Winograd for computing the discrete Fourier transform (d.f.t).
Abstract: We show how to perform a number-theoretic transform (n.t.t.) using an algorithm analogous to that of S. Winograd for computing the discrete Fourier transform (d.f.t.). Using this algorithm, the range of data lengths and word lengths is much larger than that available with conventional fast n.t.t.s.
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TL;DR: A general expression for the Fourier transform of the fault anomaly is derived in this article, which is valid for an arbitrary angle of inclination of a fault plane, by separating the gravity anomaly into a constant and a variable term.
Abstract: The application of the method of the Fourier transform in interpreting gravity anomalies of faults has so far been based upon the Fourier transform of the gravity anomaly due to a single semi‐infinite block cut by a vertical fault. A general expression for the Fourier transform of the fault anomaly is here derived which is valid for an arbitrary angle of inclination of the fault plane. For deriving the general expression, the gravity anomaly of the fault is first separated into a constant and a variable term. The transforms of the two terms are calculated separately and then added to give the general expression for the Fourier transform of the fault anomaly.
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08 Dec 1977
TL;DR: The results of this experiment suggest that image appearance may be improved by designing transform coefficient quantization rules to approximate the effects of additive noise rather than to omit low energy image components, as dictated by conventional rate-distortion theory.
Abstract: Rate-distortion theory using the mean squared error criterion is often used to design digital image coding rules. The resulting distortion is, in theory, statistically equivalent to omitting components of the image from transmission. We compare a rate-distortion simulation using the discrete cosine transform to a method which is statistically equivalent to adding uncorrelated random noise to the image. This latter method is based on a PN (pseudo-noise) transform, which is generated from a Hadamard matrix whose core consists of the cyclic shifts of a binary maximum length linear shift register sequence. Visual comparisons of the two approaches are made at the same mean squared error. In all cases, the images encoded using the PN transform method showed superior definition of detail and less geometrical distortion at transform block boundaries than the images encoded using the discrete cosine method. The results of this experiment suggest that image appearance may be improved by designing transform coefficient quantization rules to approximate the effects of additive noise rather than to omit low energy image components, as dictated by conventional rate-distortion theory.© (1977) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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01 Jan 1977TL;DR: In this paper, the authors present a companion to a tutorial session on the basic properties of the DFT which lead to Fast Fourier Transform algorithms, and discuss ways in which less well-known properties of DFT could be turned to practical use.
Abstract: This paper will be divided into two parts. The first is intended as a companion to a tutorial session on those basic properties of the DFT which lead to Fast Fourier Transform algorithms. The second part will range more widely, in particular considering ways in which certain less well-known properties of the DFT could be turned to practical use. The two parts are independent.
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01 Jan 1977TL;DR: A discrete Fourier transform module for incorpration in fast Fourier Transform processors is described, which is highly suitable for real input applications requiring high-speed transformations.
Abstract: For applications requiring high-speed and in-place treatment, it is often advantageous to realize special-purpose computers. This paper describes a discrete Fourier transform (DFT) module for incorpration in fast Fourier transform (FFT) processors. The module is highly suitable for real input applications requiring high-speed transformations. It attributes one point to all frequency channels in one clock cycle. This treatment is not only well suited for the present technology, but appears to be more attractive in view of recent trends in digital circuitry.
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22 Aug 1977TL;DR: This paper presents an efficient method to calculate two-dimensional discrete Fourier transforms over windowed regions of the light intensity matrix based on the fast Fourier transform algorithm, which can be beaten by any nonparallel algorithm.
Abstract: Computer vision systems based on general purpose computers often need efficient texture description algorithms. One common method is to calculate two-dimensional discrete Fourier transforms over windowed regions of the light intensity matrix. Although these methods described in the literature are based on the fast Fourier transform algorithm, the computation time is still too high to permit the description of texture for as many windows as are needed for good segmentation. When a set of transforms over a window at every position of the matrix is needed, an efficient method can be used. It saves information computed for previous windows and uses it to reduce the effort expended on the current window. For a window N × N and an image matrix M × M, the time complexity is reduced from O(N2M2logN) to O(N2M2). This complexity cannot be beaten by any nonparallel algorithm.
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TL;DR: In this paper, the authors described some modifications of the method rendering it applicable to asymmetrical traces, thus, for general use, in which the spectral data were limited to symmetrical traces from organic free radicals in solution.
Abstract: With the development of signal processing techniques, the spectral data obtained from analytical instruments have been collected and searched with the aid of a digital computer. Recognition of the spectrum as a wave pattern is adequate in such situations. The previous study demonstrated signal processing based on this idea, involving the discrete Fourier transform (DFT) applied to ESR spectral data, and the advantages of this method with respect to memory capacity and searching speed. In that study, however, the spectral data were limited to symmetrical traces from organic free radicals in solution, in which case the ESR spectra exhibit isotropic hyperfine structure. This paper describes some modifications of the method rendering it applicable to asymmetrical traces, thus, for general use.