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Showing papers on "Hadamard transform published in 1981"


Book
01 Jan 1981
TL;DR: This paper presents a computer program for Generating Hadamard Matrix Designs and Analyzing the Data from Such Designs and concludes with a summary of Two-Level Matrix Designs.
Abstract: Preface. Acknowledgments. FUNDAMENTALS OF EXPERIMENT DESIGN. Introduction to Experiment Design: Fundamental Concepts. Introduction to Experiment Design: Elements of Decision Making. Simple Comparative Experiments: Decisions About Population Means. Simple Comparative Experiments: Decisions About Population Variances. Sequential Experiments. TWO-LEVEL MULTIVARIABLE EXPERIMENTS. Two-Level Multivariable Experiments: Eight-Trial Hadamard Matrix Designs. Two-Level Multivariable Experiments: Hadamard Matrices Greater Than Order 8. John's Three-Quarter Fractional Factorials. Unbalanced Resolution V Designs. Resolution V Designs with Efficiency = 1. Hadamard Matrix Designs for Binomial and Poisson Responses. Summary of Two-Level Matrix Designs. A Computer Program for Generating Hadamard Matrix Designs and Analyzing the Data from Such Designs. Analysis of Goodness. Alternative Methods of Analysis. MULTILEVEL MULTIVARIABLE EXPERIMENTS. Multilevel Experiments with Qualitative Variables. Multilevel Experiments with QuantitativeVariables. Experiment Designs for Chemical Composition Experiments. Random-Strategy Experiments. RELATED TOPICS. Blocking an Experiment. Validation of Test Methods. Concepts for a Complete Project Strategy. Project Engineer's Game. Estimation of Variance. Testing Distributions. GENERAL REFERENCES, SYMBOLS, TABLES, AND ANSWERS TO EXERCISES. General References. Symbols. Tables. Answers to Exercises. Index.

118 citations


Journal ArticleDOI
TL;DR: An automatic seismic signal detection algorithm based on the Walsh transform has been developed for short-period data sampled at 20 samples/sec and tests indicate that the algorithm has a detection capability comparable to a human analyst.
Abstract: An automatic seismic signal detection algorithm based on the Walsh transform has been developed for short-period data sampled at 20 samples/sec. Since the amplitude of Walsh function is either +1 or −1, the Walsh transform can be accomplished in a computer with a series of shifts and fixed-point additions. The savings in computation time makes it possible to compute the Walsh transform and to perform prewhitening and band-pass filtering in the Walsh domain with a microcomputer for use in real-time signal detection. The algorithm was initially programmed in FORTRAN on a Raytheon Data Systems 500 minicomputer. Tests utilizing seismic data recorded in Dallas, Albuquerque, and Norway indicate that the algorithm has a detection capability comparable to a human analyst. Programming of the detection algorithm in machine language on a Z80 microprocessor-based computer has been accomplished; run time on the microcomputer is approximately 1 10 real time. The detection capability of the Z80 version of the algorithm is not degraded relative to the FORTRAN version.

62 citations


Journal ArticleDOI
TL;DR: In this paper, the authors review recent work on the stochastic approach of Walsh spectral analysis, focusing mainly on the properties of the finite Walsh transform, which in turn allow them to derive the spectral properties.
Abstract: In this paper we review recent work on the stochastic approach of Walsh spectral analysis. We are mainly interested in the properties of the finite Walsh transform, which in turn allow us to derive...

48 citations


Journal ArticleDOI
TL;DR: The techniques used in the classification of 3-(24, 12, 5) designs up to isomorphism were described and a summary of the results is contained.

47 citations


Journal ArticleDOI
TL;DR: Both 1-D and 2-D methods are developed which overcome both of the above limitations and can unite techniques used by Hadamard spectroscopy and coded aperture imaging with uniformly redundant arrays into the same mathematical basis.
Abstract: In many fields (eg, spectroscopy, imaging spectroscopy, photoacoustic imaging, coded aperture imaging) binary bit patterns known as m sequences are used to encode (by multiplexing) a series of measurements in order to obtain a larger throughput The observed measurements must be decoded to obtain the desired spectrum (or image in the case of coded aperture imaging) Decoding in the past has used a technique called the fast Hadamard transform (FHT) whose chief advantage is that it can reduce the computational effort from N2 multiplies to N log2N additions or subtractions However, the FHT has the disadvantage that it does not readily allow one to sample more finely than the number of bits used in the m sequence This can limit the obtainable resolution and cause confusion near the sample boundaries (phasing errors) We have developed both 1-D and 2-D methods (called fast delta Hadamard transforms, FDHT) which overcome both of the above limitations Applications of the FDHT are discussed in the context of Hadamard spectroscopy and coded aperture imaging with uniformly redundant arrays Special emphasis has been placed on how the FDHT can unite techniques used by both of these fields into the same mathematical basis

40 citations


Patent
Eiichi Tsuboka1
05 Aug 1981
TL;DR: In this paper, a buffer memory with the capacity equal to the number of components of an input vector to be transformed is provided and addressed in such a way computation of Hadamard transforms can be performed at faster speeds with a higher degree of efficiency.
Abstract: Devices for performing fast Hadamard transforms based upon a predetermined algorithm are provided. A buffer memory (random-access memory) with the capacity equal to the number of components of an input vector to be transformed is provided and is addressed in such a way computation of Hadamard transforms can be performed at faster speeds with a higher degree of efficiency.

24 citations


Journal ArticleDOI
TL;DR: In this paper, the authors provide a full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion using matrix differential calculus in conjunction with the Hadamard (or Schur) matrix product.
Abstract: The author provides a full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion. He uses matrix differential calculus in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented.

20 citations


Journal ArticleDOI
TL;DR: In this article, the characteristics of the Hadamard transform X-ray telescope (HTXT) were investigated and the following results were obtained: 1) The statistical error of the image reconstructed by the HTXT is uniform all over the image, which is different from the case of a pinhole camera.

17 citations


Journal ArticleDOI
TL;DR: A method for linear, one-dimensional transformations in white light is described that uses the multiplexing facility of the wavelength coordinate to achieve an image quality corresponding to the full spatial resolution of the optical system.

7 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the equivalence of Hadamard matrices can be decided in O(log 2 n) space and hence in subexponential time.
Abstract: Equivalence of Hadamard matrices can be decided inO(log2n) space, and hence in subexponential time. These resource bounds follow from the existence of small distinguishing sets.

6 citations



Journal ArticleDOI
TL;DR: The noise produced at the output of combinational logic circuits by individual gate failures is analyzed through the use of Walsh functions and results are specialized to the case where the inputs are statistically independent of the soft errors.
Abstract: The noise produced at the output of combinational logic circuits by individual gate failures is analyzed through the use of Walsh functions. Soft errors are modeled by allowing the output of each gate in a particular realization to fail temporarily, possibly introducing an error in the single binary output. The input variables also are allowed to be stochastically driven. The output probability of error contains the Walsh transform of an extended logic function and the Walsh characteristic functions of the input variables as well as the individual gate failure variables. These results are specialized to the case where the inputs are statistically independent of the soft errors. A discussion of the transform of the extended logic function is included.

Journal ArticleDOI
TL;DR: It is demonstrated that good broadcast and video-phone quality pictures can be obtained using the first four coefficients, and the first two coefficients, respectively.
Abstract: Analog and digital schemes for implementing the onedimensional Hadamard transform in real time for TV signals has been proposed. Within practical limitations, hardware has been developed and tested according to the scheme. The evaluation of the hardware has been carried out using a real image. Furthermore, bandwidthreduction experiments are conducted for various bit rates. Analog and digital transform coding schemes are compared for prominent performance parameters. It is demonstrated that good broadcast and video-phone quality pictures can be obtained using the first four coefficients, and the first two coefficients, respectively.

Journal ArticleDOI
TL;DR: In this paper, the Hadamard quotient is used to determine whether a matrix A is diagonally equivalent to an orthogonal matrix and, if so, computes the corresponding scaling factors.
Abstract: An algorithm is given which determines whether a matrix A is diagonally equivalent to an orthogonal matrix and, if so, computes the corresponding scaling factors. The algorithm makes use of the Hadamard quotient $A^{ - 1} \odiv A^t $. Such problems arise, for example, in the study of energy conserving norms for the solution of hyperbolic systems of partial differential equations.

Journal ArticleDOI
TL;DR: A novel approach for charge transfer device (CTD) implementation of the fast Walsh-Hadamard and fast Fourier transforms is presented by first expressing the Hadamard matrix as a power of a matrix, which allows for efficient CTD implementation.
Abstract: This paper presents a novel approach for charge transfer device (CTD) implementation of the fast Walsh-Hadamard and fast Fourier transforms. This is achieved by first expressing the Hadamard matrix as a power of a matrix, which allows for efficient CTD implementation. These results are then used in CTD implementation of fast Fourier transforms. The errors which accrue on using CTDs for implementing the Walsh-Hadamard transform are discussed in terms of a dispersion estimate.

Journal ArticleDOI
TL;DR: A fast digital hardware system for signal analysis and synthesis, combined with data compression or information rate reduction techniques, provides a powerful tool for a variety of control, communication and signal processing applications.

Proceedings ArticleDOI
12 Dec 1981
TL;DR: The research effort was focused on developing the Singular Value Decomposition (SVD) as an approach to image compression, and detailed comparisons were made to the two-dimensional cosine transform, Hadamard transform and Karhunen-Loeve techniques.
Abstract: The vast quantities and high generation rates of tactical imagery require very efficient data compression in order to conserve precious bandwidth for transmission and to limit the required storage volume for archiving. This paper describes the results of ef-ficiency and image quality comparisons for several transform image coding techniques. Specifically, the research effort was focused on developing the Singular Value Decomposition (SVD) as an approach to image compression. Detailed comparisons were made to the two-dimensional cosine transform, Hadamard transform and Karhunen-Loeve techniques.© (1981) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

DOI
P.D. Picton1
01 May 1981
TL;DR: A method is proposed by which binary logic functions are resolved into multithreshold form, based upon an already existing design algorithm which involves spectral translations, and can be easily adopted for CAD implementation.
Abstract: A method is proposed by which binary logic functions are resolved into multithreshold form. It is based upon an already existing design algorithm which involves spectral translations, and can be easily adopted for CAD implementation.


Journal ArticleDOI
TL;DR: An extremely simple device for the calculation of the Walsh Discrete Transform of a function which is delta modulated is presented, allowing the Transform to be calculated with very simple hardware and making the demodulation unnecessary.

01 Jan 1981
TL;DR: New algorithms and special purpose sequential processor architectures for the computation of a class of one-, two- and multi-dimensional unitary transforms are presented and it is shown that the two-dimensional FFT processor architecture proposed in this work requires less hardware than the conventional implementations.
Abstract: This work presents the development of new algorithms and special purpose sequential processor architectures for the computation of a class of one-, two- and multi-dimensional unitary transforms In particular, a technique is presented to factorize the transformation matrices of a class of multi-dimensional unitary transforms, having separable kernels, into products of sparse matrices These sparse matrices consist of Kronecker products of factors of the one-dimensional transformation matrix Such factorizations result in fast algorithms for the computation of a variety of multi-dimensional unitary transforms including Fourier, Walsh-Hadamard and generalized Walsh transforms It is shown that the u-dimensional Fourier and generalized Walsh transforms can be implemented with a u-dimensional radix-r butterfly operation requiring considerably fewer complex multiplications than the conventional implementation using a one-dimensional radix-r butterfly operation Residue number principles and techniques are applied to develop novel special purpose sequential processor architectures for the computation of one-dimensional discrete Fourier and Walsh-Hadamard transforms and convolutions in real-time The residue number system (RNS) based implementations yield a significant improvement in processing speed over the conventional realizations using the binary number system As an illustration of the factorization techniques developed in this work, novel sequential architectures of RNS-based fast Fourier, Walsh-Hadamard and generalized Walsh transform processors for real-time processing of two-dimensional signals are presented These sequential processor architectures are capable of processing large bandwidth (> 5 MHz) input sequences The application of the proposed FFT processors for the real-time computation of two-dimensional convolutions is also investigated A special memory structure to support two-dimensional convolution operations is presented and it is shown that the two-dimensional FFT processor architecture proposed in this work requires less hardware than the conventional implementations The FFT algorithms and processor architectures are verified by computer simulation

Patent
02 May 1981
TL;DR: In this paper, the color TV signal was improved by using inphase sampling points for the chrominance subcarrier of the TV signal to eliminate the influence of the color signal of a TV signal.
Abstract: PURPOSE:To improve band compressibility by eliminating an influence of the chrominance subcarrier of a color TV signal, by using inphase sampling points for the chrominance subcarrier. CONSTITUTION:The block for the Hadamard transform is formed of eight sampling points, inphase sampling points dj.1 and dj.4 on the j-th (j=1. 2...) horizontal scanning line, inphase sampling points dj+1.1 and dj+1.4 on the j+1-th horizontal scanning line, and similarly dj+2.1 and dj+2.4 and dj+3.1 and dj+3.4. Similarly, blocks are formed one after another to perform the Hadamard transform over the entire region of the screen. Thus, an influence of the color signal of a color TV signal is eliminated by selecting inphase points as sampling points to centralize frequency components of the signal at a low frequency, thereby improving band compressibility.

Journal ArticleDOI
TL;DR: A new sliding DFT circuit is proposed which is also of recursive type but does not accumulate errors, and its behavior is analyzed in detail.
Abstract: The sliding DFT algorithm is a technique for determining the DFT coefficients for time-series samples. The conventional sliding DFT circuit used in the frequency-sampling filter, however, is recursive and has an instability problem because of the accumulation of errors in the feedback path. A new sliding DFT circuit is proposed which is also of recursive type but does not accumulate errors. Its behavior is analyzed in detail. The circuit proposed is relatively simple and can easily be translated into hardware. It is also shown that a sliding Hadamard transform circuit is easily constructed, and the design of a sequence sampling filter is shown.

Journal ArticleDOI
TL;DR: Real-time one-dimensional Hadamard transform coding has been developed and the results are presented in terms of subjective quality.
Abstract: Orthogonal Transform Coding Techniques have been used as a method to compress the frequency bandwidth for TV signals. Spectrum plots have been presented for different transform codings. Real-time one-dimensional Hadamard transform coding has been developed and the results are presented in terms of subjective quality.

Patent
21 Oct 1981
TL;DR: In this paper, a color television signal is encoded by A/D converter into an eight-bit signal, and sampled values at eight sampling points of horizontal scanning lines adjoining mutually to the same horizontal scanning line, adjoining vertically and adjoining in the frame direction are stored memory 3 while the same phase relation with a chrominance subcarrier is born.
Abstract: PURPOSE:To prevent the compressibility from decreasing due to the superposition of a chrominance signal upon a luminance signal by making a prescribed array of sampling points and by increasing bits allotted to a lower sequence and decreasing bits allotted to a higher sequence respectively. CONSTITUTION:A color television signal is encoded by A/D converter 2 into an eight-bit signal, for example, and sampled values at eight sampling points of horizontal scanning lines adjoining mutually to the same horizontal scanning line, adjoining vertically and adjoining in the frame direction are stored memory 3 while the same phase relation with a chrominance subcarrier is born. Next, sampled values in one block are read out of memory 3, sampling points of Hadamard's transformation are made into blocks while the attention to the phase of the chrominance subcarrier is paid, and Hadamard transformation device 4 performs the Hadamard's transformation to find sequences h1-h8 of degree eight. Further, quantizer 5 quantizes every sequency by the best bit allotment to compress the band.

Journal ArticleDOI
TL;DR: In this paper, the pth-harmonic output of a memoryless nonlinearity with a single sinusoid as input provides enough information to compute all intermodulation products falling in the same harmonic zone.
Abstract: Ahtract-Measurement of the pth-harmonic output of a memoryless nonlinearity with a single sinusoid as input provides enough information to compute all intermodulation products falling in the same harmonic zone. For the case of two input sinusoids of arbitrary amplitudes, an integral expression (representing a weighted average of the measured characteristic) is derived for the amplitude of each output signal and any intermodulation product. Simpler expressions are obtained for the case of equal input amplitudes and for the case where one input amplitude is small. The results are applicable to bandpass nonlinearities that produce AM-to-PM as well as AM-to-AM conversion. They are applied to the cases of hard and soft limiters and to polynomial nonlinearities.

Journal ArticleDOI
TL;DR: The impulse response of a linear system may be calculated from the response to a pseudorandom sequence if the calculation is based on the fast Hadamard transform, only additions and subtractions are required.
Abstract: The impulse response of a linear system may be calculated from the response to a pseudorandom sequence. If the calculation is based on the fast Hadamard transform, only additions and subtractions are required.

Journal ArticleDOI
TL;DR: It has been concluded that the image transmission on reduced BW is economically viable and practically possible in real time.
Abstract: Digital schemes for one-dimensional Hadamard transform coding in real time has been proposed. Keeping in view the practical limitations, the hardware has been developed and tested according to the scheme. The evaluation of the hardware has been carried out using a real image. Further, the BW reduction experiment has been conducted for various bit rates. It has been concluded that the image transmission on reduced BW is economically viable and practically possible in real time.

Journal ArticleDOI
TL;DR: In this article, it was shown that if one wants the N-order H-matrix to exist, then N should be the multiple of 4. But up till now, it is not clear whether this is a sufficient condition.