Showing papers on "Hadamard transform published in 1999"

Orthogonal Arrays: Theory and Applications

Abstract: 1 Introduction.- 1.1 Problems.- 2 Rao's Inequalities and Improvements.- 2.1 Introduction.- 2.2 Rao's Inequalities.- 2.3 Improvements on Rao's Bounds for Strength 2 and 3.- 2.4 Improvements on Rao's Bounds for Arrays of Index Unity.- 2.5 Orthogonal Arrays with Two Levels.- 2.6 Concluding Remarks.- 2.7 Notes on Chapter 2.- 2.8 Problems.- 3 Orthogonal Arrays and Galois Fields.- 3.1 Introduction.- 3.2 Bush's Construction.- 3.3 Addelman and Kempthorne's Construction.- 3.4 The Rao-Hamming Construction.- 3.5 Conditions for a Matrix.- 3.6 Concluding Remarks.- 3.7 Problems.- 4 Orthogonal Arrays and Error-Correcting Codes.- 4.1 An Introduction to Error-Correcting Codes.- 4.2 Linear Codes.- 4.3 Linear Codes and Linear Orthogonal Arrays.- 4.4 Weight Enumerators and Delsarte's Theorem.- 4.5 The Linear Programming Bound.- 4.6 Concluding Remarks.- 4.7 Notes on Chapter 4.- 4.8 Problems.- 5 Construction of Orthogonal Arrays from Codes.- 5.1 Extending a Code by Adding More Coordinates.- 5.2 Cyclic Codes.- 5.3 The Rao-Hamming Construction Revisited.- 5.4 BCH Codes.- 5.5 Reed-Solomon Codes.- 5.6 MDS Codes and Orthogonal Arrays of Index Unity.- 5.7 Quadratic Residue and Golay Codes.- 5.8 Reed-Muller Codes.- 5.9 Codes from Finite Geometries.- 5.10 Nordstrom-Robinson and Related Codes.- 5.11 Examples of Binary Codes and Orthogonal Arrays.- 5.12 Examples of Ternary Codes and Orthogonal Arrays.- 5.13 Examples of Quaternary Codes and Orthogonal Arrays.- 5.14 Notes on Chapter 5.- 5.15 Problems.- 6 Orthogonal Arrays and Difference Schemes.- 6.1 Difference Schemes.- 6.2 Orthogonal Arrays Via Difference Schemes.- 6.3 Bose and Bush's Recursive Construction.- 6.4 Difference Schemes of Index 2.- 6.5 Generalizations and Variations.- 6.6 Concluding Remarks.- 6.7 Notes on Chapter 6.- 6.8 Problems.- 7 Orthogonal Arrays and Hadamard Matrices.- 7.1 Introduction.- 7.2 Basic Properties of Hadamard Matrices.- 7.3 The Connection Between Hadamard Matrices and Orthogonal Arrays.- 7.4 Constructions for Hadamard Matrices.- 7.5 Hadamard Matrices of Orders up to 200.- 7.6 Notes on Chapter 7.- 7.7 Problems.- 8 Orthogonal Arrays and Latin Squares.- 8.1 Latin Squares and Orthogonal Latin Squares.- 8.2 Frequency Squares and Orthogonal Frequency Squares.- 8.3 Orthogonal Arrays from Pairwise Orthogonal Latin Squares.- 8.4 Concluding Remarks.- 8.5 Problems.- 9 Mixed Orthogonal Arrays.- 9.1 Introduction.- 9.2 The Rao Inequalities for Mixed Orthogonal Arrays.- 9.3 Constructing Mixed Orthogonal Arrays.- 9.4 Further Constructions.- 9.5 Notes on Chapter 9.- 9.6 Problems.- 10 Further Constructions and Related Structures.- 10.1 Constructions Inspired by Coding Theory.- 10.2 The Juxtaposition Construction.- 10.3 The (u, u + ?) Construction.- 10.4 Construction X4.- 10.5 Orthogonal Arrays from Union of Translates of a Linear Code.- 10.6 Bounds on Large Orthogonal Arrays.- 10.7 Compound Orthogonal Arrays.- 10.8 Orthogonal Multi-Arrays.- 10.9 Transversal Designs, Resilient Functions and Nets.- 10.10 Schematic Orthogonal Arrays.- 10.11 Problems.- 11 Statistical Application of Orthogonal Arrays.- 11.1 Factorial Experiments.- 11.2 Notation and Terminology.- 11.3 Factorial Effects.- 11.4 Analysis of Experiments Based on Orthogonal Arrays.- 11.5 Two-Level Fractional Factorials with a Defining Relation.- 11.6 Blocking for a 2k-n Fractional Factorial.- 11.7 Orthogonal Main-Effects Plans and Orthogonal Arrays.- 11.8 Robust Design.- 11.9 Other Types of Designs.- 11.10 Notes on Chapter 11.- 11.11 Problems.- 12 Tables of Orthogonal Arrays.- 12.1 Tables of Orthogonal Arrays of Minimal Index.- 12.2 Description of Tables 12.1?12.3.- 12.3 Index Tables.- 12.4 If No Suitable Orthogonal Array Is Available.- 12.5 Connections with Other Structures.- 12.6 Other Tables.- Appendix A: Galois Fields.- A.1 Definition of a Field.- A.2 The Construction of Galois Fields.- A.3 The Existence of Galois Fields.- A.4 Quadratic Residues in Galois Fields.- A.5 Problems.- Author Index.

THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE

Abstract: We derive some inequalities of Hadamard's type for s-cdnvex functions in the second sense and give some applications connected with special means.

Methods and apparatuses for video segmentation, classification, and retrieval using image class statistical models

Abstract: Techniques for classifying video frames using statistical models of transform coefficients are disclosed. After optionally being decimated in time and space, image frames are transformed using a discrete cosine transform or Hadamard transform. The methods disclosed model image composition and operate on grayscale images. The resulting transform matrices are reduced using truncation, principal component analysis, or linear discriminant analysis to produce feature vectors. Feature vectors of training images for image classes are used to compute image class statistical models. Once image class statistical models are derived, individual frames are classified by the maximum likelihood resulting from the image class statistical models. Thus, the probabilities that a feature vector derived from a frame would be produced from each of the image class statistical models are computed. The frame is classified into the image class corresponding to the image class statistical model which produced the highest probability for the feature vector derived from the frame. Optionally, frame sequence information is taken into account by applying a hidden Markov model to represent image class transitions from the previous frame to the current frame. After computing all class probabilities for all frames in the video or sequence of frames using the image class statistical models and the image class transition probabilities, the final class is selected as having the maximum likelihood. Previous frames are selected in reverse order based upon their likelihood given determined current states.

On Universal and Fault-Tolerant Quantum Computing

Abstract: A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and ${\sigma_z}^{1/4}$), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev.

The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates

Abstract: The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach minimizes the effort to evaluate the Jacobian derivative matrix in the Newton-Raphson method for solving the resultant nonlinear formulations. In addition, the coupled nonlinear formulations for the present problems can easily be decoupled by means of the Hadamard and SJT product. Therefore, the size of the simultaneous nonlinear algebraic equations is reduced by two-thirds and the computing effort and storage requirements are alleviated greatly. Two recent approaches applying the multiple boundary conditions are employed in the present DQ nonlinear computations. The solution accuracies are improved obviously in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb efficiency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations.

Hadamard transform capillary electrophoresis.

Abstract: This paper reports the first demonstration of a multiplex sample injection technique in capillary electrophoresis. The sample was injected into a capillary (effective length, 4 cm) as a pseudorandam Hadamard sequence by a photodegradation technique using a high-power gating laser, and the fluorescence signal, which was measured using a probe excitation beam, was decoded by an inverse Hadamard transformation. The signal-to-noise ratio was improved by a factor of 8, which was in good agreement with the theoretically predicted value of 8.02. This approach is potentially useful for the enhancement of the sensitivity by 3 orders of magnitude in high-resolution capillary electrophoresis, combined with fluorescence detection.

Transform domain analysis of DES

Abstract: The Data Encryption Standard (DES) can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under the Fourier transform, Hadamard transform, extended Hadamard transform, and the Avalanche transform are investigated. Two important results about the S-boxes of DES are found. The first result is that nearly two-thirds of the total 32 functions from GF (2/sup 6/) to GF(2) which are associated with the eight S-boxes of DES have the maximal linear span G3, and the other one-third have linear span greater than or equal to 57. The second result is that for all S-boxes, the distances of the S-boxes approximated by monomial functions has the same distribution as for the S-boxes approximated by linear functions. Some new criteria for the design of permutation functions for use in block cipher algorithms are discussed.

A subband coding technique for image compression in single CCD cameras with Bayer color filter arrays

Abstract: This paper presents a subband coding technique suitable for image compression in a single CCD camera with a Bayer color filter array (CFA). In it, we have applied a SSKF (symmetric short kernel filter) both horizontally and vertically to red and blue color signals, and a two dimensional perfect reconstruction filter to green color signals. Here, we compare this technique to two other image compression methods: DPCM and the Hadamard transform, each of which also allows an output signal from the CCD in a color camera to be compressed directly with simple logic circuitry and is suitable for use in low cost video conference cameras. Simulation results demonstrate that the subband coding offers the best quality (27-30 dB) with a compression ratio of approximately 2 bit/pel.

Spectral Imaging in a Programmable Array Microscope by Hadamard Transform Fluorescence Spectroscopy

Abstract: We report the use of a thin-film transistor (TFT) twisted nematic liquid crystal spatial light modulator (SLM) for Hadamard transform two-dimensional spectral imaging in a fluorescence microscope. The liquid crystal SLM placed in the primary image plane of the microscope generates a set of spatial encoding masks defined by a cyclic S-matrix. The light passing through the mask is relayed by anamorphic optics to the entrance of an imaging spectrograph and detected with a charge-coupled device (CCD) camera. The SLM allows for the convenient generation of arbitrary masks without moving parts. The Hadamard transform approach transmits up to 50% of the light from the image field for multichannel detection, but is subject to transmission losses in the SLM. The system allows the convenient acquisition of two-dimensional spectral images. We characterized and tested many of the parameters controlling both spatial and spectral resolution, and demonstrated the system in the analysis of both naturally fluorescing and stained biological samples.

Communication methods and apparatus based on orthogonal hadamard-based sequences having selected correlation properties

Abstract: Methods and apparatus for synchronization of a transmitter and a receiver are based on orthogonal sequences having optimized correlation properties. The transmitter may generate signed versions of S-Hadamard sequences that are obtained by position-wise scrambling a set of Walsh-Hadamard sequences with a special sequence having complex elements of constant magnitude. The receiver estimates a time location and sequence identity of a received version of the synchronization signal.

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

Abstract: We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.

Family of unified complex Hadamard transforms

Abstract: Novel discrete orthogonal transforms are introduced in this paper, namely the unified complex Hadamard transforms. These transforms have elements confined to four elementary complex integer numbers which are generated based on the Walsh-Hadamard transform, using a single unifying mathematical formula. The generation of higher dimension transformation matrices is discussed in detail.

Hadamard-based soft decoding for vector quantization over noisy channels

Abstract: We present an estimator-based, or soft, vector quantizer decoder for communication over a noisy channel. The decoder is optimal according to the mean-square error criterion, and Hadamard-based in the sense that a Hadamard transform representation of the vector quantizer is utilized in the implementation of the decoder. An efficient algorithm for optimal decoding is derived. We furthermore investigate suboptimal versions of the decoder, providing good performance at lower complexity. The issue of joint encoder-decoder design is considered both for optimal and suboptimal decoding. Results regarding the channel distortion and the structure of a channel robust code are also provided. Through numerical simulations, soft decoding is demonstrated to outperform hard decoding in several aspects.

Another Proof of Kasami‘s Theorem

Abstract: We give a short direct proof for a famous theorem published by Kasami in 1971 In terms of Walsh analysis it states that for d = 2^{2k}-2^k+1 the Walsh spectrum of the Boolean function \T(x^d) on \G{2^n} consists precisely of the three values 0,\pm 2^{(n+s)/2} if s = \gcd(k,n) = \gcd(2k,n)

Video classification using transform coefficients

Abstract: This paper describes techniques for classifying video frames using statistical models of reduced DCT or Hadamard transform coefficients. When decimated in time and reduced using truncation or principal component analysis, transform coefficients taken across an entire frame image allow rapid modeling, segmentation and similarity calculation. Unlike color-histogram metrics, this approach models image composition and works on grayscale images. Modeling the statistics of the transformed video frame images gives a likelihood measure that allows video to be segmented, classified, and ranked by similarity for retrieval. Experiments are presented that show an 87% correct classification rate for different classes. Applications are presented including a content-aware video browser.

A resolution rank criterion for supersaturated designs

Abstract: Hadamard matrices are found to be useful in constructing supersaturated designs. In this paper, we study a special form of supersaturated designs using Hadamard matrices. Properties of such a supersaturated design are discussed. It is shown that the popular E(s 2 ) criterion is in general inadequate to measure the goodness of a supersaturated design. A new criterion based upon the projection property, called resolution rank (r-rank), is proposed. Furthermore, an upper bound for r-rank is given for practical use. When the number of factors is large and a small number of runs is desired, a supersaturated design can save considerable cost. A two-level supersaturated design is a fraction of a factorial design with n observations in which the number of factors k is larger than n − 1. The usefulness of such a supersaturated design relies upon the realism of effect sparsity, namely, that the number of dominant active factors is small. The goal is to identify these active factors with so-called screening experimentation. (A brief review of early work on supersaturated de- signs is available from Lin (1991).) Apart from some ad hoc procedures and computer-generated designs, the construction problem has not been addressed until very recently (see Lin (1993a) and (1995), Wu (1993), and Tang and Wu (1997)). Most of these supersaturated designs were constructed based on Hadamard matrices. In this paper, a special form of supersaturated designs using Hadamard matrices is studied. Further- more, a criterion based upon the projection property called resolution rank is proposed to further differentiate among designs.

Use of Walsh-Hadamard transform for forward link multiuser detection in CDMA systems

Abstract: A station capable of receiving information containing Walsh coding for a plurality of channels and canceling interference from the received information and the method of cancellation. A memory is provided for storing received signals containing a Walsh code for each of a plurality of channels as well as reflected and/or refracted versions of said received signals and a first plurality of signal paths is provided which are selectively coupled to the memory. The signal paths apply corresponding delays and inverse Walsh code transformations to separate the channels. Further, cancellation of the channels interfering with a desired channel proceeds with complementary delays and Walsh code transformation to regenerate the interference which is subtracted from the received signal in memory.

Proof of the Symmetry of the Off-Diagonal Heat-Kernel and Hadamard's Expansion Coefficients in General C ∞ Riemannian Manifolds

Abstract: We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds. The requirement of such a symmetry played a central role in the theory of the point-splitting one-loop renormalization of the stress tensor in either Riemannian or Lorentzian manifolds. Actually, the symmetry of these coefficients has been assumed as a hypothesis in several papers concerning these issues without an explicit proof. The difficulty of a direct proof is related to the fact that the considered off-diagonal heat-kernel expansion, also in the Riemannian case, in principle, may be not a proper asymptotic expansion. On the other hand, direct computations of the off-diagonal heat-kernel coefficients are impossibly difficult in nontrivial cases and thus no case is known in the literature where the symmetry does not hold. By approximating C∞ metrics with analytic metrics in common (totally normal) geodesically convex neighborhoods, it is rigorously proven that in general C∞ Riemannian manifolds, any point admits a geodesically convex neighborhood where the off-diagonal heat-kernel coefficients, as well as the relevant Hadamard expansion coefficients, are symmetric functions of the two arguments.

Existence of cyclic Hadamard difference sets and its relation to binary sequences with ideal autocorrelation

Abstract: Balanced binary sequences with ideal autocorrelation are equivalent to (v, k, λ)-cyclic Hadamard difference sets with v = 4n − 1, k = 2n − 1, λ = n − 1 for some positive integer n. Every known cyclic Hadamard difference set has one of the following three types of v : (1) v = 4n − 1 is a prime. (2) v is a product of twin primes. (3) v = 2n − 1 for n = 2, 3, …. It is conjectured that all cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n < 10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and the conjecture is confirmed for all v ≤ 3435. In addition, all the inequivalent cyclic Hadamard difference sets with v = 2n − 1 for n ≤ 10 are listed and classified according to known construction methods.

Method and apparatus using Walsh-Hadamard transformation for forward link multiuser detection in CDMA systems

Abstract: A mobile station suitable for multicode modulation and capable of receiving information containing Walsh coding for a plurality of channel and canceling interference from the received information and the method of cancellation. A memory is provided for storing received signals containing a Walsh code for each of a plurality of channels as well as reflected and/or refracted versions of said received signals and a first plurality of signal paths is provided which are selectively coupled to the memory, each said signal path coupled to the memory for receiving the signals stored in the memory. In each of the signal paths the received signal is delayed in accordance with a different one of a plurality of predetermined maxima of the received signal. An inverse fast Walsh transform is applied to the received signal for each channel corresponding to that channel for removing the Walsh code corresponding to that channel from said received signal. An estimate is provided for each path of phase shift and attenuation of the received signal in that path and the conjugate of the estimate is multiplied by the signal for each channel in each path after removal of the Walsh code to provide a path output for each channel. The path outputs of each of the channels are combined to provide a data estimate. The station is preferably mobile and the spaced apart condition is preferably predetermined maxima in the received signal. Interference can be further removed by applying a subtractive interference cancellation scheme.

Discrete fractional Hadamard transform

Abstract: Hadamard transform is an important tool in discrete signal processing. In this paper, we define the discrete fractional Hadamard transform which is a generalized one. The development of discrete fractional Hadamard is based upon the same spirit as that of the discrete fractional Fourier transform.

Delayless subband adaptive filtering using the Hadamard transform

Abstract: In this correspondence, an analysis of a delayless critically decimated subband adaptive filter structure is presented. In this structure, adaptive weights in each subband are computed by the LMS algorithm and then transformed into those in fullband by the Hadamard transform. It is shown that a stationary point of the proposed algorithm corresponds to the fullband Wiener filter. Some numerical results are also presented to show the performance of this scheme.

Delayless Subband Adaptive Filtering Using the Hadamard Transfrom

Abstract: In this correspondence, an analysis of a delayless critically decimated subband adaptive filter structure is presented. In this structure, adaptive weights in each subband are computed by the LMS algorithm and then transformed into those in fullband by the Hadamard transform. It is shown that a stationary point of the proposed algorithm corresponds to the fullband Wiener filter. Some numerical results are also presented to show the performance of this scheme.

HADAMARD imaging spectrometer with microslit matrix

Abstract: The concept for an imaging spectral sensor is presented. The starting point is an advanced raster scanning with multiplexing in spatial terms. The essential components are an entrance array, an imaging grating and a detector array -- a double array architecture. A programmable micro slit matrix is used as a two-dimensional HADAMARD-mask. It scans the two- dimensional images to be processed in a one-dimensional spectrometer. A multiplexing in spatial terms and simultaneously in spectral terms is possible. The spectra recorded by a commercial detector array spectrometer. At the present state the multiplexing of more than 100 spatial pixels within the quality of spectrometry is demonstrated. The concept provides a HADAMARD or multiplex advantage resulting from the micro slit matrix (increase of SNR by (root)n/2, n- number of imaging pixels) and a multidetector advantage resulting from the linear detector array of the spectrometer (increase of SNR by (root)N, N-number of detector elements). Experiments reported on a further paper.

On the choice of transforms for data hiding in compressed video

Abstract: We present an information-theoretic approach to obtain an estimate of the number of bits that can be hidden in compressed image sequences. We show how addition of the message signal in a suitable transform domain rather than the spatial domain can significantly increase the data hiding capacity. We compare the data hiding capacities achievable with different block transforms and show that the choice of the transform should depend on the robustness needed. While it is better to choose transforms with good energy compaction property (like DCT, wavelet etc.) when the robustness required is low, transforms with poorer energy compaction property (like the Hadamard or Hartley transform) are preferable choices for higher robustness requirements.

Proof of the symmetry of the off-diagonal heat-kernel and Hadamard's expansion coefficients in general $C^{\infty}$ Riemannian manifolds

Abstract: We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds. The requirement of such a symmetry played a central r\^{o}le in the theory of the point-splitting one-loop renormalization of the stress tensor in either Riemannian or Lorentzian manifolds. Actually, the symmetry of these coefficients has been assumed as a hypothesis in several papers concerning these issues without an explicit proof. The difficulty of a direct proof is related to the fact that the considered off-diagonal heat-kernel expansion, also in the Riemannian case, in principle, may be not a proper asymptotic expansion. On the other hand, direct computations of the off-diagonal heat-kernel coefficients are impossibly difficult in nontrivial cases and thus no case is known in the literature where the symmetry does not hold. By approximating $C^\infty$ metrics with analytic metrics in common (totally normal) geodesically convex neighborhoods, it is rigorously proven that, in general $C^\infty$ Riemannian manifolds, any point admits a geodesically convex neighborhood where the off-diagonal heat-kernel coefficients, as well as the relevant Hadamard's expansion coefficients, are symmetric functions of the two arguments.