Showing papers on "Hadamard transform published in 1978"
TL;DR: Hadamard matrices have been widely studied in the literature and many of their applications can be found in this paper, e.g., incomplete block designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III (SRSIII), optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects.
Abstract: An $n \times n$ matrix $H$ with all its entries $+1$ and $-1$ is Hadamard if $HH' = nI$. It is well known that $n$ must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard matrices exist for every $n$ which is a multiple of 4. The smallest order for which a Hadamard matrix has not been constructed is (as of 1977) 268. Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, especially during the last three decades. These matrices can be transformed to produce incomplete block designs, $t$-designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III designs, optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects. In this paper we survey the existence of Hadamard matrices and many of their applications.
288 citations
TL;DR: In this article, it was shown that if a scalar field has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere.
Abstract: In the point-splitting prescription for renormalizing the stress-energy tensor of a scalar field in curved spacetime, it is assumed that the anticommutator expectation valueG(x, x′)=〈o(x)o(x′)+o(x′)o(x)〉 has a singularity of the Hadamard form asx→x′. We prove here that ifG(x,x′) has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere, i.e., Cauchy evolution preserves the Hadamard singularity structure. In particular, in a spacetime which is flat below a Cauchy surface, for the “in” vacuum stateG(x,x′) is of the Hadamard form everywhere, and thus the point-splitting prescription in this case has been rigorously shown to give meaningful, finite answers.
239 citations
TL;DR: A real-time image processor which is capable of video compression using either the sequency-ordered Walsh-Hadamard transform (WHT)W, or the discrete cosine transform (DCT), is considered, which results in substantial savings in the number of multiplications and additions required to obtain the DCT, relative to its direct computation.
Abstract: A real-time image processor which is capable of video compression using either the sequency-ordered Walsh-Hadamard transform (WHT)W, or the discrete cosine transform (DCT), is considered. The processing is done on an intraframe basis in (8 X 8) data blocks. The (WHT)W coefficients are computed directly, and then used to obtain the DCT coefficients. This is achieved via an (8 X 8) transformation matrix which is orthonormal, and has a block-diagonal structure. As such, it results in substantial savings in the number of multiplications and additions required to obtain the DCT, relative to its direct computation. Some aspects of a hardware implementation of the processor are also included.
55 citations
TL;DR: A conference matrix of order n is a square matrix C with zeros on the diagonal and ± 1 elsewhere, which satisfies the orthogonality condition CCT = (n − 1)I as mentioned in this paper.
Abstract: A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CCT = (n — 1)I. If in addition C is symmetric, C = CT, then its order n is congruent to 2 modulo 4 (see [5]). Symmetric conference matrices (C) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [1; 5; and 7, pp. 293-400]. We shall require several definitions.
45 citations
TL;DR: The concept of energy packing efficiency of the Walsh-Hadamard transform is extended to other discrete orthogonal transforms and it is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.
Abstract: The concept of energy packing efficiency (EPE) of the Walsh-Hadamard transform (WHT) first proposed by Kitajima [1], is extended to other discrete orthogonal transforms. The concept as a criterion for evaluating the transforms is discussed. It is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.
36 citations
28 citations
TL;DR: It is shown that existing systems for this translation, e.g., those in which a fast Fourier transform (FFT) processor is used, can be derived from this generalized scheme as special cases.
Abstract: A generalized scheme for an all-digital time-division multiplex (TDM) to frequency-division multiplex (FDM) translator is discussed. It is shown that existing systems for this translation, e.g., those in which a fast Fourier transform (FFT) processor is used, can be derived from this generalized scheme as special cases. Several new Implementations can also be derived from this scheme when different processors are used. A specific example using a Hadamard processor is discussed.
23 citations
TL;DR: Results by Marshall Hall on integral completions of matrices satisfying orthogonality conditions are extended as far as possible, with special attention given to the Hadamard case.
21 citations
01 Jan 1978
TL;DR: A general class of even/odd transforms, including the Karhunen-Loeve transform, the discrete cosine transform, and the Walsh-Hadamard transform, is presented in this paper.
Abstract: A general class of even/odd transforms is presented that includes the Karhunen-Loeve transform, the discrete cosine transform, the Walsh-Hadamard transform, and other familiar transforms. The more complex even/odd transforms can be computed by combining a simpler even/odd transform with a sparse matrix multiplication. A theoretical performance measure is computed for some even/odd transforms, and two image compression experiments are reported.
21 citations
TL;DR: This paper analyzes the systematic errors in Hadamard transform optical instruments caused by moving masks, incorrect mask alignment, faulty mask fabrication, missing data, diffraction, etc. and describes techniques for reducing or eliminating these errors.
Abstract: Error sources encountered in Hadamard transform optical instruments are discussed Such errors are caused by factors including moving masks, incorrect mask alignment, defects in mask fabrication, missing data, drifts in background level, and diffraction Techniques for error reduction and/or elimination are described for each of the cases considered It is noted that the errors described occur in singly encoded spectrometers and imagers
TL;DR: A special class of Universal Logic Gate is described, whose programming is determined by external connections to the function variables and states 0, 1 only, and a method of determining this class under the Walsh transform is given.
Abstract: A special class of Universal Logic Gate (ULG) is described, whose programming is determined by external connections to the function variables and states 0, 1 only. Preliminary results indicate that the number of external connections required for this class of ULG is smaller than that of conventional ULG'S. A method of determining this class under the Walsh transform is given. Related applications in read-only-memories, sequential and intelligent machines are discussed.
TL;DR: A method to establish a chromatogram by pseudo random injections and the Hadamard transform technique is described, finding that it is possible to accumulate a peak from a detector output signal, superimposed by background noise.
Abstract: A method to establish a chromatogram by pseudo random injections and the Hadamard transform technique is described. It is possible to accumulate a peak from a detector output signal, superimposed by background noise. The method is tested on simulated process.
01 Jan 1978
TL;DR: In this article, the basic principles behind the advantages of Fourier and Hadamard transform methods in spectroscopy were introduced, using a minimum of instrumental detail, and applications of these principles to each of several branches of Spectroscopy, along with illustrative examples.
Abstract: This chapter is intended to introduce, using a minimum of instrumental detail, the basic principles behind the advantages of Fourier and Hadamard transform methods in spectroscopy. Applications of these principles to each of several branches of spectroscopy, along with illustrative examples, may be found in succeeding chapters.
TL;DR: The Walsh-Hadamard transform or (WHT) cs is useful in mapping an even or odd sequence since, in this case, at least one-half of the transform components will be zero.
Abstract: Walsh-Hadamard matrices are rearranged such that the first half of the rows represents cal functions in increasing order of sequency whereas the second half represents sal functions in decreasing order of sequency. The transform based on this rearrangement is called the Cal-Sal Walsh-Hadamard transform or (WHT) cs . General expressions for developing the elements of these matrices are developed. These matrices are decomposed into sparse matrix factors which lead directly to the fast algorithms similar to those for other forms of the WHT. The (WHT) cs is useful in mapping an even or odd sequence since, in this case, at least one-half of the transform components will be zero.
TL;DR: The notion of "invariants" within the power spectrum of one-dimensional transformations is developed and the specific case of some widespread transformations is considered and a character recognition experiment using the invariants obtained is presented.
Abstract: This correspondence presents a device for designing unitary transformations based on the Hadamard transform process. The notion of "invariants" within the power spectrum of one-dimensional transformations is developed and the specific case of some widespread transformations is considered. The results are extended to two-dimensional transformations and a character recognition experiment using the invariants thus obtained is presented.
TL;DR: A sequency difference detection and correction (s.d.c.c.) system is described which enables the partial correction of transmission errors in a Walsh-Hadamard transform image to be achieved without channel coding.
Abstract: A sequency difference detection and correction (sddc) system is described which enables the partial correction of transmission errors in a Walsh-Hadamard transform image to be achieved without channel coding Using a first-order two-dimensional random Gaussian Markov field as the image, the percentage mean-square error in the recovered signal is reduced with the aid of the sddc system by two orders of magnitude for transmission error rates <3%
TL;DR: This paper presents a reasonable alternative to traditional Fourier analysis by proposing the use of the Fast Walsh Transform, and problems as phase sensitivity and general acceptability of the Walsh power spectrum are discussed.
01 Jan 1978
TL;DR: Seberry and Seberry as mentioned in this paper showed that for every odd integer q there exists an integer t (dependent on q) so that there is a skewHadamard matrix of order 2tq.
Abstract: Recently I have proved that for every odd integer q there exists integers t and s (dependent on q) so that there is an Hadamard matrix of order 2tq and a symmetric Hadamard matrix with constant diagonal order 2s q2. We conjecture that "for every odd integer q there exists an integer t (dependent on q) so that there is a skewHadamard matrix of order 2tq”. This paper makes progress toward proving this conjecture. In particular we prove the result when q = 5 (mod 8) = s2 + 4r2 is a prime power and all orthogonal designs of type (l, a, b, c, c+│r│), where 1+a+b+2c+│r│ = 2t, exist in order 2t. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J, On skew Hadamard matrices, Ars. Combinatoria, 6, 1978, 255-276. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/988 ON SKEW HADAMARD MATRICES
TL;DR: In this article, the role of the Walsh-Hadamard transform (WHT) in extracting prime implicants is discussed, which is pertinent to the overall minimization problem.
Abstract: The Walsh-Hadamard transform (WHT) provides a one-to-one mapping of n-variable Boolean functions onto an n-dimensional transform space. As such, it enables synthesis procedures to be carried out in the transform domain. This short paper discusses the role of the WHT in extracting prime implicants, which is pertinent to the overall minimization problem. First, a procedure to identify all the prime implicants of a 1-vertexl located at the origin is developed by inspecting the elements of a single inverse transform. Second, a theorem is proved to show how the signs of the transform coefficients can be changed, to obtain all the prime implicants of an arbitrazy 1-vertex via the same inverse transforn operation.
01 Jan 1978
TL;DR: A spectrometer sorts electromagnetic radiation into its component colors, each color corresponds to a particular value of a parameter, and the resulting spectrum displays the intensity of radiation for each value of this parameter as discussed by the authors.
Abstract: A spectrometer sorts electromagnetic radiation into its component colors. Each color corresponds to a particular value of a parameter—wavelength, energy, or frequency—and the resulting spectrum displays the intensity of radiation for each value of this parameter.
TL;DR: In this article, the Walsh-Hadamard transform method is applied to the covering problem and a modification of the prime implicants as binary variables is proposed to identify all complete covers by inspecting the elements of an inverse transform.
Abstract: Transform methods and dyadic groups have been used for the classification of Boolean functions as well as for prime implicant determination. In a recent paper a prime implicant extraction method, based on Walsh-Hadamard transform methods, was presented. It processes the true minterms of the function separately, one at a time. In this paper this transform method is applied to the covering problem. Taking the prime implicants as binary variables a slight modification of the prime-implicant extraction method allows one to identify all complete covers by inspecting the elements of an inverse transform. Redundant forms can be detected and rejected easily. Another method for the determination of all irredundant covers classifies the 2m elements of the dyadic group of element length m as incomplete, redundant or irredundant covers, m beingthe number of prime implicants. A version for hand-worked problems is given, as well as a computer-oriented version.
TL;DR: In this paper, the distributions of Hadamard coefficient for blocks of size 8 × 1 picture elements in six 625-line television pictures were obtained, and the data were well approximated by gamma distributions.
Abstract: The distributions of Hadamard coefficient for blocks of size 8 × 1 picture elements in six 625-line television pictures were obtained. The data were well approximated by gamma distributions. Low-sequency components were best fitted by choosing ?(n) with n in the range 1/2?2/3, and high-sequency components by n = 1 (equivalent to the negative exponential distribution).
TL;DR: The results of an extensive investigation of the properties of 64-point Hadamard-Haar transformed speech are presented, with detailed information being provided about the probability-density functions of the Haar coefficients, about the average power-density spectrum in Haar domain, and about the autocorrelation function of speech reconstructed from a limited number of haar coefficients as discussed by the authors.
Abstract: This paper reports on the combined application of the Hadamard and Haar transforms as a method of speech coding. The results of an extensive investigation of the properties of 64-point Hadamard-Haar transformed speech are presented, with detailed information being provided about the probability-density functions of the Haar coefficients, about the average power-density spectrum in the Haar domain, and about the autocorrelation function of speech reconstructed from a limited number of Haar coefficients. A preliminary series of listening tests have been performed and they confirm the conclusions drawn from the statistical properties of the transformed speech. The preliminary listening tests indicate that intelligible, though somewhat noisy, speech can be obtained at bit rates of approximately 3.5kbit/s.
01 Jan 1978
TL;DR: Conditions under which distinct (+1,−1) sequences have the same nonperiodic autocorrelation function are studied.
Abstract: Nonperiodic autocorrelation functions of integer sequences have been studied in connection with Hadamard matrices and combinatorial designs. Here we study conditions under which distinct (+1,−1) sequences have the same nonperiodic autocorrelation function. These conditions involve the Hadamard (tensor) product of sequences and the concatenation of sequences. Generating functions for the non-periodic autocorrelation functions are used to prove the main results of this paper.
TL;DR: In this paper, it was shown that H(l) is the absolute value of the determinant of an easily written down matrix whose only entries are 0 and 1, and the best known upper and lower bounds for small l.
TL;DR: The relationship between the Gibbs differential of the first kind and the classic Boolean Difference is detailed and an extension of the method to accommodate indeterminate states is considered.
TL;DR: It is shown that, for determining the frequency of gut rhythms, simple filtering and signal conditioning preceding the microprocessor dispenses with the need for analogue to digital conversion, and a very simple digital microprocessing system for the continuous monitoring of Gut rhythms has been produced.
Abstract: The use of Fourier transforms based on orthogonal sinusoidal functions is well established in the analysis of spectral components in noisy medical signals. In this paper the use of Walsh transformations based on orthogonal discrete signals is described for the analysis of ‘slow-wave’ rhythms in the gastro-intestinal tract of mammals. The Walsh transform approach has the advantage that very fast algorithms can be developed since multiplications involving sinusoidal functions are replaced by additions and subtractions. These algorithms are very suitable for simple microprocessors and it is shown that, for determining the frequency of gut rhythms, simple filtering and signal conditioning preceding the microprocessor dispenses with the need for analogue to digital conversion. Hence a very simple digital microprocessing system for the continuous monitoring of gut rhythms has been produced. It has also been extended to provide filtering of signals via forward and inverse Walsh transforms.
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20 Jul 1978
TL;DR: In this article, the reference signal which is appleid to a phase detector circuit from the input part of one position lock loop through an Hadamard converter circuit was used to make the correction of a fixed time difference possible with applying to plural channels.
Abstract: PURPOSE:To make the correction of a fixed time difference possible with applying to plural channels by giving the reference signal which is appleid to a phase detector circuit from the input part of one position lock loop through an Hadamard converter circuit.