Showing papers on "Hadamard transform published in 1980"

The Stability of Inverse Problems

Abstract: Many inverse problems arising in optics and other fields like geophysics, medical diagnostics and remote sensing, present numerical instability: the noise affecting the data may produce arbitrarily large errors in the solutions. In other words, these problems are ill-posed in the sense of Hadamard.

Progressive transmission of grey-scale and binary pictures by simple, efficient, and lossless encoding schemes

Abstract: Efficient, simple, and lossless methods for encoding and transmitting grey-scale and binary (B/W) pictures are described. The methods are such that an initial segment of the transmission permits the receiving device to construct an approximate picture; as transmission proceeds, the receiver progressively constructs better approximations. Some of the low-bandwidth channel usages include telebrowsing -where one wants to abort transmission of unwanted pictures as soon as they are recognized, and teleconferencing-where one wants to receive a gestalt first, followed by the details. In the method for grey-scale pictures, the transmitter first defines a hierarchical structure of picture subdivisions, and assigns, simply by table lookup, approximate average light values to all pairs of cells from the smallest size to that encompassing the entire picture. During tranmission the latter "primary" value is sent, followed by numbers which permit successive cell splitting, thus producing progressively finer picture representations in approximate values, culminating in an exact reconstruction at the pel level. A picture of p pels quantized into b bits each is perfectly reconstructed upon receipt of exactly b × p bits. If the recipient deems an intermediate version satisfactory, then "picture compression" is effectively achieved. This scheme thus provides some of the benefits of transform encoding (Fourier, Hadamard, Hotelling, singular-value decomposition) but with no truncation error and no need for handling coefficients of various sizes. Furthermore, computation varies only linearly with number of pels. The method for binary (B/W) pictures also involves a hierarchical structuring of the picture but with attention paid to picture compression-by declaring subdivisions, at as high a level as possible, to be solid black or solid white (and in need of no further description). Compressions thus achieved are 8:1 in cases where the "blob" coding method of Frank gives 11½:1

Topographic feature extraction using sensor array system

Abstract: A method and apparatus for topographic feature extraction by masking a video signal representation of an optical image using a two-dimension Walsh function is disclosed. The optical energy of an image is converted into a video signal. A Walsh function signal in accordance with a two-dimension Walsh is generated. The video signal is multiplied with the Walsh function signal to produce a Walsh transform coefficients signal indicative of the decomposed spectral components of the image. The method and apparatus can further include providing selected topographical feature signals in accordance with the Walsh transform coefficients of selected topographic features. A selected topographical feature can be detected by comparing the Walsh transform coefficients signal with the selected topographical feature signals. The Walsh transform coefficients signal is unique to the selected topographical feature being detected.

On the spectral decomposition of stationary time series using walsh functions. II

Abstract: The paper looks at the asymptotic properties of the finite Walsh–Fourier transform applied to a discrete-time stationary time series, and shows that in many ways we have analogous results to those obtained when using the finite trigonometric Fourier transform.

Composite Spectra and the Analysis of Switching Circuits

Abstract: A method is given for the evaluation of the Rademacher–Walsh spectra of the Boolean sum, product, and EXCLUSIVE-OR of two functions without reintroducing the Rademacher–Walsh transform. The results are derived using a general coding scheme and depend heavily upon the use of a dyadic convolution operation.

Hadamard Transform Spectroscopy

Abstract: Fourier Transform Interferometry has become a useful tool in infrared spectroscopy. These instruments require very exacting optics and mechanical alignments which require micrometer accuracy in mirror alignments and the measurement of mirror displacement. Because of these required low tolerances, interferometers are very expensive and require constant calibration.

Waveform synthesis via inverse Walsh transform

Abstract: The dominant-term concept in representing arbitrary functions using Walsh series is described. To verify dominant-term concept, a Fast Walsh Transform/Inverse Fast Walsh Transform (FWT/1FWT) subroutine following Brown's algorithm and an Approximato IFWT (AIFWT) subroutine have been written in FORTRAN IV and applied to various functions. The results obtained aro quito satisfactory. Based upon the dominant-torm concept, an inexpensive, fully digital, programmable waveform synthesizer lias beon designed and implemented. The various waveforms obtained from the aynthesiier coincide with the results obtaind from computer simulation.

Image spectrum analyzer for cartographic feature extraction

Abstract: An image spectrum analyzer and method for cartographic feature extraction comprising an image, means for generating a Walsh function light pattern and for illuminating the image with the Walsh function light pattern to procuce a masked pattern, and means for receiving the masked pattern and for producing an electrical signal in accordance with same. A digital signal can be provided in accordance with the electrical signal, and a digital data processor under stored program control can provide a Walsh transform coefficient representative of the digital signal. More than one Walsh function light pattern can be generated by the apparatus and method of the present invention to produce more than one masked pattern, and representative Walsh coefficient. The Walsh coefficients can be used to perform cartographic feature extraction of the image.

A model of distributed type associative memory with quantized Hadamard transform

Abstract: This paper proposes a new correlation matrix network model of associative memory in brain. Each memorized pattern which consists of binary (+1 or-1) elements is preprocessed by a quantized Hadamard transform to increase selectivity. The association ability of a correlation matrix network model depends on the orthogonality between key patterns by which the corresponding memorized patterns are associatively recalled. In a brain model, however, it is rare that the key patterns are mutually orthogonal since they are memorized patterns themselves. The quantized Hadamard transform, presented in this paper, renders the memorized patterns approximately orthogonal. The model is tested by computer simulation.

Picture signal coding process system

Abstract: PURPOSE:To ensure the high compression to the picture signals with addition of a small number of circuits by varying the coding bit number according to the nature of the DC-AC conversion block and then distributing the bit number to each component of the predictive error signals. CONSTITUTION:The picture input given from terminal 1 is converted into the digital signals through A/D converter 2 and then applied to Hadamard converter 3 to deliver Hadamard conversion output YN. This output YN is applied to one side of subtractor circuit 4, and then output EN of circuit 4 is applied to mode selector 5 and quantizer 6. The absolute value of the predictive error signal is compared with the prescribed threshold level by selector 5. And then the mode division is given to several units of signals which are under the threshold level simultaneously from the low frequency component among the predictive error signals which are given ordering from the low to high frequency components, thus one mode being selected. Then the control is given to the characteristics of quantizer 6 via selector 5, and at the same time the transmission code is produced at coder 7 by the output of selector 5 as well as output ZN of quantizer 6 to be transmitted to the transmission line.

Higher dimensional orthogonal designs and hadamard matrices

Abstract: We construct n-dimensional orthogonal designs of type (1,1)n, side 2 and propriety (2,2,…,2). These are then used to show that orthogonal designs of type (2t,2t)n, side 2t+1 and propriety (2,2,…,2) exist.

Phase corrected video recording system

Abstract: A video tape recording apparatus with the use of an Hadamard transformation system is disclosed. The apparatus comprises means for distributing the video signal to a plurality of channels, means for recording and reproducing the distributed video signals by plurality of magnetic heads, means for synchronizing a time-base correction signal for time-base correction with a sampling signal for Hadamard transformation, and means for phase-controlling a sampling signal for Hadamard inverse transformation to the time-base correction signal in phase.

A recurrent issue on the extended Nyquist Array

Abstract: A large number of papers have appeared in recent years on the use of generalized row sums and generalized column sums in the extended version of the Rosenbrock Nyquist Array design scheme for multivariable systems Some of the authors claim that their results using these row/ column sums encompass similar results using the Hadamard property of irreducible complex matrices It is the purpose of this note to indicate that such claims are false On the contrary, all these results are direct consequences of the Hadamard property and can be deduced from standard results in M-matrix theory

Channel division recording/reproducing apparatus

Abstract: A channel division recording/reproducing apparatus is provided for dividing an input signal into signals for a plurality of channels through an Hadamard transformation, frequency modulating the signals of the respective channels and recording them and, after demodulating the recorded signals for the respective channels, subjecting the demodulated signals to an Hadamard inverse transformation and reproducing the input signal. Out of the Hadamard-transformed signals, the signal on the channel of the minimum frequency band is separated by a filter from the input signal and the separated signal processed by an additional Hadamard transformer and Hadamard inverse transformer and frequency modulated with a modulation index greater than the original signal and with a carrier of a lower frequency. An impovement in signal-to-noise ratio is thereby obtained. When recording a video signal, the "beat" phenomenon between the video signal and carrier signal is reduced while the signal-to-noise ratio of the video signal as a whole is improved.

Some applications of Good's theorem (Corresp.)

Abstract: Three applications of a theorem of I. J. Good are made: a simplification of the fast Hadamard transform algorithm of R.R. Green used in the decoding of first-order Reed-Muller codes, a simple proof of the well-known Parseval formula, and an application to the discrete one-dimensional Fourier transform.

Hadamard Gap Series and Normal Functions

Abstract: X f(z) = £ ckz" k where nk + l/nk ^ q > 1. Then f is normal if and only if f is Bloch if and k = 0 only if Mm sup \ck\ < co. J. S. Hwang [3] has proved the above theorem in the special case where ck = n'k" for some m > 1 and (nk+x/nk) -> GO as k -> oo. The proof of Theorem 1 is based on ideas of W. Fuchs and techniques which go back to Hardy and Littlewood. Throughout the remainder of the paper p0 will denote the maximum of 2 log 20/{q — 1 —log q) and log 10/(log q — 1 +q~). Consider the associated real valued function F defined by

Use Of Curved Slits To Increase Throughput Of A Hadamard Spectrometer

Abstract: The throughput of a Hadamard spectrometer is directly proportional to the length of the slits. However, optical aberrations limit the slit length that can be used. The usable length of curved and straight slits are theoretically and experimentally compared for a typical singly encoded Hadamard spectrometer that has a Czerny-Turner plane-grating mounting. For this Hadamard spec-trometer the optical throughput can be increased by a factor of ten by using properly curved slits.

A useful property of the coefficients of a Walsh-Hadamard transform

Abstract: It has been found that the coefficients of the Walsh-Hadamard transformation of a vector composed of integers have the interesting property of being all even or all odd. The following presents a proof of this property and suggests an application to data compression.

Motion-Adaptive TV Data Compression

Abstract: Based on digitized TV frames a computer simulation study was conducted on a motion -adaptive TV data compression scheme, defined as one in which a 2- dimensional transformapplied to subblocks is followed by the transmission to the receiving site of only changedsubblocks. Performance was measured both by calculation of Normalized Mean Square Errorand by subjective viewing of reconstructed frames. Two systems designs leading to 512x512resolution operation (one based on the Hadamard and one on the Discrete Cosine Transform)were prepared.IntroductionThe motion -adaptive TV data compression described herein is more effective than conven-tional intraframe techniques because it encompasses them and furthermore takes advantageof the correlation between frames by updating only those subblocks which have changed.Following a 2 -D transform performed on small (e.g. 8x8) subblocks, intraframe compressionis achieved by assigning a small number of bits (or none) to each transform coefficient.This bit allocation is made adaptive by assigning fewer bits to those subblocks within aframe which exhibit less busyness or activity. Next, motion -adaptivity, a form of inter -frame compression, is provided by having the amount of change in coefficients between thecurrent subblock and the corresponding subblock of the previous frame determine which trans-form subblocks to transmit. This process has been simulated and an approach to hardwareimplementation derived.BackgroundTwo -dimensional transforms combined with frame to frame motion -adaptivity achieve highcompression ratios because they exploit pixel correlation in all three dimensions.

Some infinite classes of Hadamard matrices

Abstract: A recursive method of A. C. Mukhopadhay is used to obtain several new infinite classes of Hadamard matrices. Unfortunately none of these constructions give previously unknown Hadamard matrices of order <40,000. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J, Some infinite families of Hadamard matrices, J Austral Math Soc, Ser. A, 29, 1980, 235-242. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1002