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Showing papers on "Hadamard transform published in 1990"


Patent
24 Aug 1990
TL;DR: In this paper, a sub-band coder for video signals is disclosed, which uses sets of two-tap finite impulse response (FIR) filters having equal-magnitude coefficients to decompose the video signal at multiple stages.
Abstract: A sub-band coder for video signals is disclosed, which is easily realizable in VLSI due to its simple structure. The coder uses sets of two-tap finite impulse response (FIR) filters having equal-magnitude coefficients to decompose the video signal at multiple stages. In the preferred embodiment the sub-band coder has an asymmetrical structure. With the arrangement, the sub-band decomposition effects what is equivalent to a multiple block-size Hadamard transform of the video signal in which coefficients are transmitted from various block-sized transforms of larger blocks of pixel data.

83 citations


PatentDOI
TL;DR: In this article, the product relationships are coded by a Hadamard differences method, where the combined daughter spectrum of a selected half of the precursors is subtracted from the combined spectrum of the remaining precurors, so that no ions are lost.
Abstract: The simultaneous collection of multiple spectra using tandem and multidimensional mass spectrometry from multiple precursors yields correspondingly enhanced sensitivity through Hadamard transform deconvolution. For MS n spectra, the product relationships are coded by a Hadamard differences method wherein the combined daughter spectrum of a selected half of the precursors is subtracted from the combined daughter spectrum of the remaining precursors, so that no ions are lost.

75 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe the application of Hadamard transform Raman microscopy to the imaging of edge plane microstructures in laser-modified highly ordered pyrolitic graphite (HOPG) electrodes.
Abstract: In this communication, we describe the application of Hadamard transform Raman microscopy to the imaging of edge plane microstructures in laser-modified highly ordered pyrolitic graphite (HOPG) electrodes. Hadamard transform Raman microscopy is a highly selective method of analysis which can image thermally sensitive materials at micron-scale spatial resolution. The technique is capable of imaging relatively weak Raman scatterers in only a few minutes. The current multichannel microscope generates images having 255 × 256 pixels. In addition, we characterize an imaging artifact present in our current system, as well as apply a first-order correction for the problem.

60 citations


Journal ArticleDOI
TL;DR: In this paper, a procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources, viz., a sphere, a horizontal cylinder, and a 2-D vertical prism of large depth extent.
Abstract: Walsh functions are a set of complete and orthonormal functions of nonsinusoidal waveform. In contrast to sinusoidal waveforms whose amplitudes may assume any value between -1 to +1, Walsh functions assume only discrete amplitudes of + or -1 which form the kernel function of the Walsh transform. Because of this special nature of the kernel, computation of the Walsh transform of a given signal is simpler and faster than that of the Fourier transform. The properties of the Fourier transform in linear time are similar to those of the Walsh transform in dyadic time. The Fourier transform has been widely used in interpretation of geophysical problems. Considering various aspects of the Walsh transform, an attempt has been made to apply it to some gravity data.A procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources, viz., a sphere, a horizontal cylinder, and a 2-D vertical prism of large depth extent. The technique has been applied to data from the published literature to evaluate its applicability, and the results are in good agreement with the more conventional ones.

59 citations


Journal ArticleDOI
TL;DR: In this paper, a Hadamard transform Raman microscope was used for multichannel detection and spatial multiplexing with spectral resolution of 0.6 μm per pixel.
Abstract: Spatial multiplexing is combined with multichannel detection in a Hadamard transform Raman microscope which provides 127 × 128 pixel images with 12 cm−1 spectral resolution. Spatial resolution of 0.6 μm per pixel has been achieved. A spatial multiplex advantage of better that 104 is demonstrated. Instrumental design details and spectroscopic images are presented.

55 citations


Journal ArticleDOI
TL;DR: In this paper, a new Hadamard spectroscopic imaging (HSI) technique based on transverse magnetization encoding is presented and tested experimentally using average Hamiltonian theory, and conditions under which a proper combination of gradients and RF functions can produce, as a good approximation, a plane rotation whose flip angle is the Fourier transform of the RF function even in the presence of chemical shift and B0 inhomogeneity.

48 citations


Journal ArticleDOI
TL;DR: A novel type of algorithms for the discrete sine transform (DST) are introduced, using a basic trigonometric identity, to realize a successive reduction of the summation size in a simple manner, and therefore cause a very simple structure.

33 citations


Journal ArticleDOI
TL;DR: It is shown that if an abelian group G contains a Hadamard difference set, then certain subgroups of G must also contain Hadamards difference sets, allowing the known nonexistence theorems for HadamARD difference sets to be extended to many more groups.

31 citations


Journal ArticleDOI
TL;DR: The ill-posed problem of analytic continuation is regularized by a prescribed bound and the numerical error is shown to be consistent with that prescribed by the three-circles principle of Hadamard.
Abstract: The ill-posed problem of analytic continuation is regularized by a prescribed bound. A simple computer algorithm is given that is based on the fast Fourier transform. The algorithm computes m complex values and a positive error bound with time complexity $O(m\log m)$. As a function of the data errors and the prescribed bound, the numerical error is shown to be consistent with that prescribed by the three-circles principle of Hadamard.

31 citations


Journal ArticleDOI
R. Forré1
TL;DR: The design of S-boxes with minimal mutual information between input and output subvectors (considered as random variables) is investigated and an algorithm to construct functions with good entropy profiles is presented.
Abstract: The design of S-boxes with minimal mutual information between input and output subvectors (considered as random variables) is investigated. First, the conditional entropy of the value of a boolean function conditioned on its random arguments is expressed as a function of the Walsh transform of the function. The entropy profile of a function is then defined; it allows the comparison of functions with regard to their (conditional) entropies. An algorithm to construct functions with good entropy profiles is then presented. It consists of a stepwise improvement of randomly chosen functions and uses the relation between the Walsh transform and the (conditional) entropies of a function. The statistical independency of boolean functions is investigated in the final section.

31 citations


Journal ArticleDOI
TL;DR: In this article, the algebraic structure of linearly recursive sequences under the Hadamard product was described and the invertible elements and zero divisors were characterized using Hopf algebras.
Abstract: We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.

01 Jan 1990
TL;DR: Seberry and Yamada as discussed by the authors introduced the concept of M-structures to unify and generalize a number of concepts in Hadamard matrices including Williamson matrices, Goethals Seidel matrices and generalized quaternion matrices.
Abstract: The new concept of M-structures is used to unify and generalize a number of concepts in Hadamard matrices including Williamson matrices, Goethals-Seidel matrices, Wallis-Whiteman matrices and generalized quaternion matrices. The concept is used to find many new symmetric Williamson-type matrices, both in sets of four and eight, and many new Hadamard matrices. We give as corollaries "that the existence of Hadamard matrices of orders 4g and 4h implies the existence of an Hadamard matrix of order 8gh" and "the existence of 'Williamson type matrices of orders u and v implies the existence of 'Williamson type matrices of order 2uu". This work generalizes and utilizes the work of Masahiko Miyamoto and Mieko Yamada. Lists of odd orders < 1000 for which Hadamard and Williamson type matrices are known are given. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Yamada, M, Products of Hadamard, Williamson and other orthogonal matrices using Mstructures, Proceedings of Combinatorics Conference, Kobe, Japan, November, 1989. This conference paper is available at Research Online: http://ro.uow.edu.au/infopapers/1044 [135J K Jennifer Seberry and Mieko Yamada, Products of Hada'm' ard,' th h Williamson and o er art agonal matrices using M-structures, Proceedings 1 C b· enee, Kobe, Japan, November 1989. 0 om matonc3 ConferProducts of Hadamard Matrices, "Williamson Matrices and Other Orthogonal Matrices using


Journal ArticleDOI
TL;DR: In this paper, a Sinc quadrature rule is presented for the evaluation of Hadamard finite-part integrals of analytic functions, and special treatment is given to integrals over the interval (?1,1).
Abstract: A Sinc quadrature rule is presented for the evaluation of Hadamard finite-part integrals of analytic functions. Integration over a general are in the complex plane is considered. Special treatment is given to integrals over the interval (?1,1). Theoretical error estimates are derived and numerical examples are included.

Book ChapterDOI
01 Nov 1990
TL;DR: The paper deals with an examination of exponent permutations with respect to their non-linearity and examines the interrelation between non- linearity and Walsh transform.
Abstract: The paper deals with an examination of exponent permutations with respect to their non-linearity. The first part gives the necessary background to be able to determine permutation non-linearity. The second examines the interrelation between non-linearity and Walsh transform. The next part summarizes results gathered while experimenting with different binary fields. In the last part of the work, we discuss the results obtained and questions which are still open.

Proceedings ArticleDOI
21 Mar 1990
TL;DR: Two algorithms for the calculation of the forward Hadamard-Walsh transform for completely and incompletely specified Boolean functions using the properties of a disjoint-cube-array representation of Boolean functions are described.
Abstract: The authors describe two algorithms for the calculation of the forward Hadamard-Walsh transform for completely and incompletely specified Boolean functions. The first method is based on direct manipulation from Karnaugh maps. The conversion starts from Karnaugh maps and results in Hadamard-Walsh spectral coefficients. The second algorithm makes use of the properties of a disjoint-cube-array representation of Boolean functions. >

Journal ArticleDOI
TL;DR: The complete enumeration of all inequivalent extremal doubly-even codes derived from Hadamard matrices of order 20 is given.

ReportDOI
27 Feb 1990
TL;DR: A unified approach to the design and evaluation of fast algorithms for discrete signal processing is developed based on the theory of finite groups, which includes the familiar cases of the fast Fourier and Walsh- Hadamard transforms but also reveals a large variety of novel methods.
Abstract: : A unified approach to the design and evaluation of fast algorithms for discrete signal processing is developed. Based on the theory of finite groups, it hence includes the familiar cases of the fast Fourier and Walsh- Hadamard transforms. However, the use of noncommutative groups reveals a large variety of novel methods. Some of these exhibit a superior performance, as measured by both reduced error rates and computational complexity, on nonstationary data. The recent history of this subject is reviewed first, followed by a detailed examination of the three principal ingredients of the present study: the underlying groups, the signal-processing tasks on which the group-based algorithms are to compete, and the signal models used to define the data environment. Test results and conclusions then follow, the former being based on the use of random correlation matrices. (kr)

Journal ArticleDOI
TL;DR: The applicability of the recursive Walsh-Hadamard transformation to FIR and IIR (finite-and infinite-impulse-response) filtering is investigated in this paper, using a common structure for recursive transforms recently introduced by G. Peceli (1986), the usual frequency-domain FIR filtering problem can be easily converted into a Walsh sequency-domain filtering problem.
Abstract: The applicability of the recursive Walsh-Hadamard transformation to FIR and IIR (finite- and infinite-impulse-response) filtering is investigated. It is shown that using a common structure for recursive transforms recently introduced by G. Peceli (1986), the usual frequency-domain FIR filtering problem can be easily converted into a Walsh sequency-domain filtering problem. It is also shown that a simple modification of this structure results in a possible alternative for IIR filter implementations. >

Journal ArticleDOI
TL;DR: In this paper, a block diagram description of HTS and the spectrum-recovery process is presented and a computer simulation of this model has been developed and can be used to examine the effects of certain nonidealities that may typically be encountered.
Abstract: The multiplex advantage offered by Hadamard transform spectrometry (HTS) can improve the signal-to-noise ratio (SNR) at the output of a spectrometer. However, additional processing of the spectrometer output is required to recover the individual spectral components. A block diagram description of HTS and the spectrum-recovery process is presented. A computer simulation of this model has been developed and can be used to examine the effects of certain nonidealities that may typically be encountered. Traditionally, the inverse Hadamard transform (IHT) has been used as the spectrum-recovery method, but the IHT does not take into account the nonidealities associated with the multiplexing process. Two spectrum-recovery methods that address the problems of nonidealities are presented. The relative performance of all three methods is compared with regard to mean square error (MSE) and the computational efficiency of the algorithms necessary to implement the schemes. An example application is described, and the performance of the three spectrum-recovery schemes is discussed. >

Journal ArticleDOI
TL;DR: In this article, three spectrum-recovery techniques for an HT spectrometer having a nonideal electro-optic mask are considered in terms of the mean-square error (MSE) associated with a given estimate.
Abstract: The multiplexing inherent in the Hadamard transform (HT) spectrometer can result in an improved spectrum-estimate when the detector is the major source of noise. A spectrum-estimate may be further improved by taking into account any nonidealities in the system. In this paper, observations concerning the errors associated with such estimates are presented, with the use of results obtained from computer simulations. Three spectrum-recovery techniques for an HT spectrometer having a nonideal electro-optic mask are considered in terms of the mean-square error (MSE) associated with a given estimate. The discussion of the MSE is with respect to the input spectrum to be estimated, the detector noise, the transmittances of the nonideal mask, and the use of coaddition. Included is a review of the computational efficiency and the statistical bias of each method. The relative performances of the spectrum-recovery methods are presented with examples to help identify the sources of error for each of the techniques.


Book ChapterDOI
05 Nov 1990
TL;DR: An infinite sequence of even self-dual codes based on Hadamard matrices is constructed that is conjectured to satisfy the requirements of long binary block codes.
Abstract: After proving that long binary block codes having the same error exponent as optimum codes (those that attain the minimum possible probability of error) have binomial distance distribution, an infinite sequence of even self-dual codes based on Hadamard matrices is constructed that is conjectured to satisfy the requirements. The first two codes in the sequence are the extended Hamming [8,4,4] and Golay [24,12,8] codes.

Proceedings ArticleDOI
01 May 1990
TL;DR: A subband-based coding scheme for the digital transmission of advanced television (ATV) signals within broadband ISDN (BISDN) is described, which achieves the roughly 5.6:1 compression desired while retaining very high image quality.
Abstract: A subband-based coding scheme for the digital transmission of advanced television (ATV) signals within broadband ISDN (BISDN) is described. It is intended for the delivery of high-quality video to the home or office at the CCITT recommended H4 rate of roughly 130 Mb/s. The scheme uses intrafield processing only, resulting in relatively low complexity for hardware implementation, very desirable error propagation properties and the elimination of motion-related artifacts. The use of the shortest kernal (two-tap) quadrature mirror filter (QMF) pairs for signal decomposition and reconstruction minimizes quantization noise spread and further reduces complexity. Through successive QMF operations, the signal is decomposed into six bands to achieve low noise coding not normally associated with the shortest kernal implementations. In effect, the coding scheme is identical to a Hadamard transform (HT) with nonconstant block sizes. When combined with entropy coding, this approach achieves the roughly 5.6:1 compression desired while retaining very high image quality. >

Journal ArticleDOI
01 Jan 1990-Talanta
TL;DR: A liquid-crystal spatial light-modulator Hadamard transform spectrometer is adapted for multielemental atomic spectrochemical analysis and the flame emissions of alkali metals are studied as a preliminary example.

Journal ArticleDOI
TL;DR: Hadamard matrices with maximum excess are constructed for the following cases: m = 8, 13, 18, and σ(n) is the maximum excess of an Hadamard matrix of order n.

Journal ArticleDOI
TL;DR: In this article, the ideal boundary of a Hadamard manifold is defined to be the equivalence classes of rays, defined by Busemann [Bu], which is not symmetric in general.
Abstract: In this paper we study the ideal boundaries of surfaces admitting total curvature as a continuation of [Sy2] and [Sy3]. The ideal boundary of an Hadamard manifold is defined to be the equivalence classes of rays. This equivalence relation is the asymptotic relation of rays, defined by Busemann [Bu]. The asymptotic relation is not symmetric in general. However in Hadamard manifolds this becomes symmetric. Here it is essential that the manifolds are focal point free.

Proceedings ArticleDOI
05 Apr 1990
TL;DR: A neural network model for invariant object recognition using backpropagation learning and competitive learning is presented and the technique of moment invariants for feature extraction is investigated.
Abstract: The authors introduce a new class of artificial neural network (ANN) models based on transformed domain feature extraction. Many optical and/or digital recognition systems based on transformed domain feature extraction are available in practice. Optical systems are inherently parallel in nature and are preferred for real time applications, whereas digital systems are more suitable for non-linear operations. In their ANN models the authors combine advantages of both digital and optical systems. Many transformed domain feature extraction techniques have been developed during the last three decades. They include: the Fourier transform (FT), the Walsh Hadamard transform (WHT), the discrete cosine transform (DCT), etc. As an example, the authors have developed ANN models using the FT and WHT domain features. The models consist of two stages, the feature extraction stage and the recognition stage. The authors use back-propagation and competitive learning algorithms in the recognition stage. They use these ANN models for invariant object recognition. The models have been used successfully to recognize various types of aircraft, and also have been tested with test patterns. >

Journal ArticleDOI
TL;DR: An algorithm of a simple systolic array processor for the HT ( hadamard transform) is presented, based on the HCG (Hadamard coefficient generator), which provides high pipelining rates.
Abstract: An algorithm of a simple systolic array processor for the HT (Hadamard transform) is presented. It is based on the HCG (Hadamard coefficient generator). The HCG makes the signs of the Hadamard matrix (HM) elements and the matrixvector multiplication is executed. This algorithm is simple and provides high pipelining rates.

Proceedings ArticleDOI
01 Apr 1990
TL;DR: The implementation of a software texture analysis technique for images based on the entropy of transform components is described, resulting in a relative texture measure that reflects regional variations of texture.
Abstract: The implementation of a software texture analysis technique for images based on the entropy of transform components is described. Different images were compared by computing their entropies, resulting in a relative texture measure. Since entropy can be based on the statistics of both gray-level components and frequency components, four entropy computation routines were implemented. The software calculates the entropy of the gray-levels histogram, the frequency components using the fast-Fourier transform (FFT), transform components using the discrete-cosine transform (DCT), and the transform coefficients of the fast-Hadamard transform (FHT). Because of its decrease in computation time and storage requirements, fast Hadamard was chosen as a better transformation. Entropy calculations were tested on different regional sizes in a time-varying imaging system in order to study regional variations of texture. >