Showing papers on "Hadamard transform published in 1975"
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TL;DR: In this paper, the Williamson type and Goethals-Seidel matrices were combined by introducing F-matrices, which are a generalization of both Williamson and GSE matrices, for the new orders 119, 171, 185, 217 and the new classes 1 4 q(q + 1), q ≡ 3(mod 8) a prime power and 1 2 p(p − 3), p ≡ 1(mod 4) and p − 4 both prime powers.
126 citations
TL;DR: A hybrid version of the Haar and Walsh-Hadamard transforms (HT and WHT) called Hadamard-Haar transform (HHT), is defined and developed and its utility and effectiveness are compared with other discrete transforms on the basis of some standard performance criteria.
Abstract: A hybrid version of the Haar and Walsh-Hadamard transforms (HT and WHT) called Hadamard-Haar transform (HHT),is defined and developed. Efficient algorithms for fast computation of the (HHT), and its inverse are developed. (HHT)r is applied to digital signal and image processing and its utility and effectiveness are compared with other discrete transforms on the basis of some standard performance criteria.
55 citations
Patent•
[...]
TL;DR: In this article, the first Hadamard coefficient, called H1, equals the sum of the picture element signals, and the control signal is employed to predict H1 and the predictor control signal was thereafter used for coding H1.
Abstract: In PCM and DPCM systems, a Hadamard orthogonal transformation of picture element signals is known to offer a means for reducing the bit rate for transmission of the signals. The first Hadamard coefficient, called H1, equals the sum of the picture element signals. Accordingly, still further reduction in the transmission bit rate can be achieved by efficiently coding H1. The disclosed coder includes a control signal generator for providing a control signal corresponding to a predetermined function of the quantized Hadamard coefficient signals. Several illustrative arrangements are disclosed. In three arrangements, the respective control signals are employed to adaptively select one of a plurality of quantizers, the selected quantizer for coding H1. In a fourth arrangement, the control signal is employed to predict H1, the predictor control signal being thereafter used for coding H1.
47 citations
32 citations
Patent•
02 Jun 1975TL;DR: In this article, line and edge features on the peripheral segments of a two dimensional data scene are classified by data manipulations in the Hadamard transform domain, and one dimensional transform coefficients which uniquely determine the classifications are extracted through weighting by submatrices characteristic of the peripheral segment.
Abstract: Line and edge features on the peripheral segments of a two dimensional data scene are classified by data manipulations in the Hadamard transform domain. One dimensional transform coefficients which uniquely determine the classifications are extracted through weighting by submatrices characteristic of the peripheral segments.
30 citations
01 Jan 1975
TL;DR: This chapter is devoted to the study of the Walsh-Hadamard transform (WHT), which is perhaps the most well-known of the nonsinusoidal orthogonal transforms.
Abstract: This chapter is devoted to the study of the Walsh-Hadamard transform (WHT), which is perhaps the most well-known of the nonsinusoidal orthogonal transforms. The WHT has gained prominence in various digital signal processing applications, since it can essentially be computed using additions and subtractions only. Consequently its hardware implementation is also simpler.
24 citations
Patent•
31 Mar 1975TL;DR: In this article, a machine for generating sequency ordered Walsh transform coefficients from an input data sequence comprises an ordered cascade of identically configured signal processor modules, each of which receives two sequential ordered transform blocks of Walsh transform co-efficients and by alternately adding and subtracting corresponding elements in those blocks produces the transform coefficients of next higher order.
Abstract: A machine for generating sequency ordered Walsh transform coefficients from an input data sequence comprises an ordered cascade of identically configured signal processor modules. Each module receives two sequency ordered transform blocks of Walsh transform co-efficients and by alternately adding and subtracting corresponding elements in those blocks produces the transform co-efficients of next higher order.
24 citations
TL;DR: An improved computational algorithm for the Hadamard transform and the R transform is described, by performing the computation "in place", the number of storage locations is minimized and the speed is increased.
Abstract: This correspondence describes an improved computational algorithm for the Hadamard transform and the R transform. By performing the computation "in place", the number of storage locations is minimized and the speed is increased. The transformed coefficients are in the order of increasing sequency.
22 citations
21 citations
TL;DR: The purpose of this paper is to add yet another class of Hadamard matrices to the ever growing list of constructions, and to prove the following results.
20 citations
Patent•
16 Jan 1975
TL;DR: In this paper, a video recording system with a plurality of fixed recording and/or playing-back magnetic heads has been described, in which a video signal with a wide frequency band is converted using an Hadamard conversion circuit, to a small number of narrow band signals, each of which is recorded and played back by each fixed head.
Abstract: A video recording system with a plurality of fixed recording-and/or-playing-back magnetic heads has been disclosed. A video signal with a wide frequency band is converted using an Hadamard conversion circuit, to a plurality of narrow band signals. Each narrow band signal is recorded and played back by each fixed head. The Hadamard conversion circuit is very simple in structure and can be provided with digital switching circuits and adders or integrators.
Patent•
IBM1
TL;DR: In this paper, an improved Hadamard filter is disposed between the dispersive element and detector of a hadamard transform spectrometer, which has a series of linear photoactive diode elements arranged in the focal plane of an array of optical lenses.
Abstract: An improved Hadamard filter is disposed between the dispersive element and detector of a Hadamard transform spectrometer. The detector has a series of linear photo-active diode elements arranged in the focal plane of an array of optical lenses. The lenses may be a series of Fly's-Eye lenses with each series arranged to overlay the corresponding linear element of the detector, or may be a cylindrical lens overlying a corresponding detector element. Individual lenses of the Fly's-Eye lens or individual elements of the cylindrical lens are selectively masked according to the desired matrix so as to perform the Hadamard transform spectrometry.
Patent•
07 May 1975
TL;DR: In this article, the amplitude of picture points in a line-by-line picture signal was determined by generating selected elements of a basis vector associated with each coefficient in a Hadamard matrix and, for each element, forming a product of the coefficient and a factor determined according to the value of the element.
Abstract: Method and apparatus for generating amplitudes of picture points in a line-by-line picture signal for a display device from subpicture information encoded as coefficients of a Hadamard transform. Amplitudes of the picture points in a line are determined by generating selected elements of a basis vector associated with each coefficient in a Hadamard matrix and, for each element, forming a product of the coefficient and a factor determined according to the value of the element. Each element and the product determined therefrom relate to a picture point. All the products for each picture point are added to give the amplitude for that point.
TL;DR: In this paper, a Hadamard transform spectrometer (HTS) was constructed, which simultaneously obtains fifteen ir spectra, each having 255 spectral elements, in real time through use of a minicomputer with 8K words of memory and a CRT display.
Abstract: We have constructed a Hadamard transform spectrometer (HTS) which simultaneously obtains fifteen ir spectra, each having 255 spectral elements. Spectra are obtained essentially in real time through use of a minicomputer with 8K words of memory and a CRT display. This permits operation of the instrument in the field.
TL;DR: The problems of developing an optical system to perform image Hadamard transforms are discussed and the possibilities of the suggested method for image coding are noted.
Abstract: The problems of developing an optical system to perform image Hadamard transforms are discussed. The method involves parallel-successive calculations of the elements of the matrix of spectral components resulting from the decomposition of an initial image into Walsh functions. The basic unit of the optical system realizing this method is an integrator representing a projecting optical system with defocusing in one of the directions. The procedure of the choice of the parameters of such a unit pulse response is described, and the experimental results are given. The matrix of 8 × 8 spectral components was calculated. The calculation error is equal to 1.5–2%. The possibilities of the suggested method for image coding are noted.
01 Jan 1975
TL;DR: A fast algorithm is presented for a two-dimensional transform of a data matrix such as Fourier or Hadamard transforms that can be applied to a matrix, which is too large for the main storage and is stored sequentially rowwise in an auxiliary storage.
Abstract: A fast algorithm is presented for a two-dimensional transform of a data matrix such as Fourier or Hadamard transforms. It can be applied to a matrix, which is too large for the main storage and is stored sequentially rowwise in an auxiliary storage. The size of the matrix may be of Rmrows and of arbitrary number of columns. Whenever R rows of working area are available in the main storage, the matrix is read out, processed, and stored back m times. This new algorithm does not require the presently used method of transposing the data matrix.
TL;DR: In this article, a simple relationship between the BIFORE phase spectrum and the modified Hadamard transform (MHT) coefficients is established, and it is also pointed out that given the power spectrum and phase spectrum for circular shifts of 0 to (N/2 - 1), the input data can be reconstructed.
Abstract: A fast method for calculating the BIFORE phase spectrum for different circular shifts of the input data is developed. A simple relationship between the BIFORE phase spectrum and the modified Hadamard transform (MHT) coefficients is established. It is also pointed out that given the BIFORE power spectrum and the phase spectrum for circular shifts of 0 to (N/2 - 1), the input data can be reconstructed.
TL;DR: In this article, the propagation of plane waves in generalized thin elastic rods is analyzed and relations between Hadamard stability and criteria that wave frequencies be real are obtained. And certain design estimates for Hadamards stability in helical and straight rods are also presented.
30 Oct 1975
TL;DR: A real-time digital video processor using Hadamard transform techniques to reduce video bandwidth is described and algorithms related to spatial compression, temporal compression, and the adaptive selection of parameter sets are described.
Abstract: A real-time digital video processor using Hadamard transform techniques to reduce video bandwidth is described. The processor can be programmed with different parameters to investigate various algorithms for bandwidth compression. The processor is also adaptive in that it can select different parameter sets to trade off spatial resolution for temporal resolution in the regions of the picture that are moving. Algorithms used in programming the system are described along with results achieved at various levels of compression. The algorithms relate to spatial compression, temporal compression, and the adaptive selection of parameter sets.© (1975) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this paper, changes in the Hadamard transform of a vector are investigated under two conditions: (i) shifting the elements of the vector cyclically for 2l places and (ii) interchanging any two elements.
Abstract: Changes in the Hadamard transform of a vector are investigated under two conditions: 1) shifting the elements of the vector cyclically for 2lplaces and 2) interchanging any two elements of the vector. The two-dimensional case is also investigated including shifting and interchanging of rows or columns.
TL;DR: In this paper, the authors obtained sufficient conditions for the univalence of continuously differentiable mappings f(z) of plane domains which, in the case of conformal mappings, reduce to both well known and new results.
Abstract: Using two methods, quasiconformal continuation involving a theorem of Hadamard and direct estimation of f(z2)−f(z1), we obtain sufficient conditions for the univalence of continuously differentiable mappings f(z) of plane domains which, in the case of conformal mappings, reduce to both well-known and new results.
TL;DR: In this article, the classification of Boolean functions of order n, n ≤ 5, under the Rademacher-Walsh transform, together with the operation of spectral translation, is examined.
Abstract: Some new results showing the classification of Boolean functions of order n, n ≤ 5, under the Rademacher–Walsh transform, together with the operation of spectral translation, are examined. It is found that there are 48 prototype functions, of which 21 are threshold functions. Examination of the canonic spectral forms of these threshold functions shows that a threshold function may be identified uniquely for n ≤ 5, under a sum-of-squares criterion.
TL;DR: It is shown that using this algorithm, one can compute the slant transform by means of a simple modification of the same Cooley-Tukey algorithm which is used to compute the Hadamard ordered Walsh-Hadamard transform.
Abstract: A Cooley-Tukey algorithm for the slant transform and its inverse is developed It is shown that using this algorithm, one can compute the slant transform by means of a simple modification of the same Cooley-Tukey algorithm which is used to compute the Hadamard ordered Walsh-Hadamard transform
30 Oct 1975
TL;DR: The relationship between computational speed and the resolution and frame rate of television imagery that may be transform encoded using the different methods is illustrated and it is shown that for picture element (pixel) rates up to 5 MHz the N2 computation is the more economical to implement.
Abstract: Several different hardware configurations for implementing the Hadamard transform in real-time are discussed. The discussion is referenced to a 64 point (8 x 8) transform that is used in image coding for bandwidth reduction. A successive implementation of two 8 point transformations with intermediate random access memory using the straight forward N2 computation is compared to implementations of the Fast Hadamard Transform (FHT). The speed of computing transform coefficients is compared to the hardware requirements of the various techniques. The relationship between computational speed and the resolution and frame rate of television imagery that may be transform encoded using the different methods is illustrated. It is shown that for picture element (pixel) rates up to 5 MHz the N2 computation is the more economical to implement.
TL;DR: In this paper, a technique has been developed to get a large number of nonisomorphic solutions of a (4t+3, 2t+1, t) design.
Abstract: A technique has been developed to get a large number of nonisomorphic solutions of a (4t+3, 2t+1, t) design. Some results are proved on the conjecture for Hadamard matrices.
TL;DR: A discussion is given of two functions of the entries of a square matrix, both related to Hadamard's determinant theorem, which have some merits as alternatives to norm-bound “condition numbers.”
Abstract: A discussion is given of two functions of the entries of a square matrix, both related to Hadamard's determinant theorem, which have some merits as alternatives to norm-bound “condition numbers.” One (for linear systems) is known; the other (for eigensystems) seems to be new.
TL;DR: A simple, versatile Hadamard‐transform computer is described by using fast CMOS dynamic shift registers as memory elements, computation speed is high, and transformation takes place during the measurement.
Abstract: This paper describes a simple, versatile Hadamard‐transform computer. By using fast CMOS dynamic shift registers as memory elements, computation speed is high, and transformation takes place during the measurement. The apparatus can also be used as a signal averaging computer.
TL;DR: It is shown that the cyclic correlation between two Walsh functions is identically zero except if they have equal "Contradegrees."
Abstract: It is shown that the cyclic correlation between two Walsh functions is identically zero except if they have equal "Contradegrees."