Showing papers on "Hadamard transform published in 1995"

Some inequalities of Hadamard type

Abstract: A sharp Hadamard s inequality is proved for the class of functions introduced by Godunova and Levin A new class P I of quasi convex functions on an interval I is introduced f I R belongs to P I i for all x y I and f x y f x f y and a sharp Hadamard s inequality is proved for that class The results obtained can e g be applied for the class of nonnegative monotone functions and some applications are pointed out Introducton Let I a b be an interval on the real line let f I R be a convex function and let a b I a b We consider the well known Hadamard s inequality f a b b a Z b

Quadratic regularization functionals for phase unwrapping

Abstract: The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.

Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

Abstract: The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.

New classes of finite unimodular sequences with unimodular Fourier transforms. Circulant Hadamard matrices with complex entries

Abstract: New classes of finite unimodular sequences with unimodular Fourier transforms. Circulant Hadamard matrices with complex entries.

Generation of Cocyclic Hadamard Matrices

Abstract: The theory of cocyclic development of designs is applied to binary matrices, and an algorithm for generating cocyclic binary matrices is outlined. The eventual goal is to generate and classify all cocyclic Hadamard matrices of small side, in terms of an underlying group G and a cocycle f : G × G → Z 2. Preliminary results are presented and open problems are posed.

Method and apparatus for remotely calibrating a phased array system used for satellite communication using a unitary transform encoder

Abstract: A method and apparatus for remotely calibrating a system having a plurality of N elements, such as a phased array system, is provided. The method includes generating coherent signals, such as a calibration signal and a reference signal having a predetermined spectral relationship between one another. The calibration signal which is applied to each respective one of the plurality of N elements can be orthogonally encoded using a unitary transform encoder that uses a predetermined transform matrix, such as a Hadamard transform matrix or a two-dimensional discrete Fourier transform matrix, to generate a set of orthogonally encoded signals. The set of orthogonally encoded signals and the reference signal are transmitted to a remote location. The transmitted set of orthogonally encoded signals is coherently detected at the remote location. The coherently detected set of orthogonally encoded signals is then decoded using the inverse of the predetermined encoding matrix to generate a set of decoded signals. The set of decoded signals is then processed for generating calibration data for each element of the phased array system.

Adiabatic Vacua and Hadamard States for Scalar Quantum Fields on Curved Spacetime

Abstract: Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. Using techniques from the theory of pseudodifferential operators and wavefront sets on manifolds a criterion for a state to be an Hadamard state is developed. It is shown that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.

The Hadamard Product and Some of its Applications in Statistics

Abstract: Algebraic properties of the Hadamard product are used to establish some statistical properties.

Fourier and Hadamard: Transforms in spectroscopy

Abstract: Discussion of mathematical transformations, focussing on the Hadamard transform, with comparisons to Fourier transform.

A soft decoder vector quantizer for a Rayleigh fading channel: application to image transmission

Abstract: A Hadamard-based framework for soft decoding in vector quantization over a Rayleigh fading channel is presented. We also provide an efficient algorithm for decoding calculations. The system has relatively low complexity, and gives low transmission rate since no redundant channel coding is used. Our image coding simulations indicate that the soft decoder outperforms its hard decoding counterpart. The relative gain is larger for bad channels. Simulations also indicate that encoder training for hard decoding suffices to get good results with the soft decoder.

Defining Sets for Block Designs: An Update

Abstract: This paper deals with the following question: how many, and which, blocks of a design with given parameters must be known before the remaining blocks of the design are uniquely determined? We survey the theoretical background on such defining sets, some specific results for smallest and other minimal defining sets for small designs and the techniques used in finding them, the few known results on minimal defining sets for infinite classes of designs, and the conjectures on minimal defining sets for some classes of Hadamard designs.

Applications of Multi-Terminal Binary Decision Diagrams

Abstract: Functions that map boolean vectors into the integers are important for the design and verification of arithmetic circuits. MTBDDs and BMDs have been proposed for representing this class of functions. We discuss the relationship between these methods and describe a generalization called hybrid decision diagrams which is often much more concise. The Walsh transform and Reed-Muller transform have numerous applications in computer-aided design, but the usefulness of these techniques in practice has been limited by the size of the boolean functions that can be transformed. Currently available techniques limit the functions to less than 20 variables. In this paper, we show how to compute concise representations of the Walsh transform and Reed-Muller transform for functions with several hundred variables. We show how to implement arithemetic operations efficiently for hybrid decision diagrams. In practice, this is one of the main limitations of BMDs since performing arithmetic operations on functions expressed in this notation can be very expensive. In order to extend symbolic model checking algorithms to handle arithmetic properties, it is essential to be able to compute the BDD for the set of variable assignments that satisfy an arithmetic relation. Bryant and Chen do not provide an algorithm for this. In our paper, we give an efficient algorithm for this purpose. Moreover, we prove that for the class of linear expressions, the time complexity of our algorithm is linear in the number of variables. Our techniques for handling arithmetic operations and relations are used intensively in the verification of an SRT division algorithm similar to the one that is used in the Pentium.

On the complete pivoting conjecture for a hadamard matrix of order 12

Abstract: This paper settles a conjecture by Day and Peterson that if Gaussian elimination with complete pivoting is performed on a 12 by 12 Hadamard matrix, then (1,2,2,4,3,10/3,18/5,4,3,6,6,12) must be the (absolute) pivots. Our proof uses the idea of symmetric block designs to reduce the complexity that would be found in enumerating cases. In contrast, at least 30 patterns for the absolute values of the pivots have been observed for 16 by 16 Hadamard matrices. This problem is non-trivial because row and column permutations do not preserve pivots. A naive computer search would require (12!)2 trials.

The structure of weighing matrices having large weights

Abstract: We examine the structure of weighing matricesW(n, w), wherew=n−2,n−3,n−4, obtaining analogues of some useful results known for the casen−1. In this setting we find some natural applications for the theory ofsigned groups and orthogonal matrices with entries from signed groups, as developed in [3]. We construct some new series of Hadamard matrices from weighing matrices, including the following:W(n, n−2) implies an Hadamard matrix of order2n ifn≡0 mod 4 and order 4n otherwise;W(n, n−3) implies an Hadamard matrix of order 8n; in certain cases,W(n, n−4) implies an Hadamard matrix of order 16n. We explicitly derive 117 new Hadamard matrices of order 2 t p, p<4000, the smallest of which is of order 23·419.

Recursive relationships, fast transforms, generalisations and VLSI iterative architecture for Gray code ordered Walsh functions

Abstract: Two Walsh transforms in Gray code ordering are introduced. The generation of two Walsh transforms in Gray code ordering from the binary code is shown. Recursive relationship between higher and lower matrix orders for Gray code ordering of Walsh functions, using the concepts of operator matrices with symmetric and shift copy, are developed. The generalisation of the introduced Gray code ordered Walsh functions for arbitrary polarity is shown. Another recursive algorithm for a fast Gray code ordered Walsh transform, which is based on the new operators on matrices, joint transformations and a bisymmetrical pseudo-Kronecker product, is introduced. The latter recursive algorithm is the basis for the implementation of a constant-geometry iterative architecture for the Gray code ordered Walsh transform. This architecture can be looped n times or cascaded n times to produce a useful VLSI integrated circuit.

DCT image compression and motion compensation using the hadamard transform

Abstract: The objective of this invention is to provide a data processor which can perform motion estimation of moving images at high speed and high accuracy. The data processor according to this invention is equipped with Hadamard transformer (110), first stage processor (120), second stage processor (130), and motion compensation circuit (140). The Hadamard transformer (110) receives image data (12) of the current frame and image data (34) of the reference frame, and Hadamard transforms this image data. First stage processor (120) block matches the target block with the Hadamard coefficient of the reference frame using multiple low-frequency coefficients selected from the Hadamard transformed data. Second stage processor (130) refers to the block matching position obtained in first stage processor (120), determines the search range in the picture data of the reference frame, and obtains the motion vector of the target block in said search range. Motion compensation circuit (140) outputs picture data which was motion compensated on the basis of the motion vector.