Showing papers on "Hadamard transform published in 1982"

Fourier, Hadamard, and Hilbert Transforms in Chemistry

Abstract: Advantages of Transform Methods in Chemistry.- Hadamard and Other Discrete Transforms in Spectroscopy.- Processing Software for Fourier Transform Spectroscopies.- Dispersion versus Absorption (DISPA): Hilbert Transforms in Spectral Line Shape Analysis.- Fourier Transform Ion Cyclotron Resonance Spectroscopy.- Fourier Transform Nuclear Quadrupole Resonance Spectroscopy.- Fourier Transform Dielectric Spectroscopy.- Pulsed Fourier Transform Microwave Spectroscopy.- Two-Dimensional Fourier Transform NMR Spectroscopy.- Endor Spectroscopy by Fourier Transformation of the Electron Spin Echo Envelope.- Advances in FT-NMR Methodology for Paramagnetic Solutions: Detection of Quadrupolar Nuclei in Complex Free Radicals and Biological Samples.- Fourier Transform ?SR.- Fourier Transform Infrared Spectrometry.- Aspects of Fourier Transform Visible/UV Spectroscopy.- Fourier Transform Faradaic Admittance Measurements (FT-FAM): A Description and Some Applications.- Optical Diffraction by Electrodes: Use of Fourier Transforms in Spectroelectrochemistry.- List of Contributors.

Self-Clutter Cancellation and Ambiguity Properties of Subcomplementary Sequences

Abstract: In radar signal design it is well known that a fixed volume under the ambiguity surface representing signal energy can only be shifted but not eliminated in the delay-Doppler plane because of the constraint imposed by Woodward's total volume invariance. Rihaczek has shown that periodic signal repetition, though appealing to increased energy, increases the time-bandwidth product at the expense of introducing pronounced ambiguities in the delay-Doppler plane, and thus self-clutter is generated when signals are repeated in the time domain to increase energy. The undesirable self-clutter has a masking effect on targets in different resolution cells thereby limiting performance. An analysis is presented to show that a class of waveforms described in an earlier paper as the subcomplementary set of sequences which are basically repetitive and Hadamard coded, exhibit the property of cancelling self-clutter completely in the delay-Doppler plane if their ambiguity functions are combined. By this technique it is possible to repeat contiguously a basic waveform N times in a prescribed manner to increase signal energy and to cancel totally the resulting self-clutter by combining the ambiguity functions of N different repetitive waveforms which are Hadamard coded. A convenient matrix method to combine the ambiguity functions of subcomplementary sequences, which is an extension of known methods to derive the ambiguity function of repetitive waveforms, is presented. Radar implementation considerations and comparison of performance with various forms of linear frequency modulation (FM) are also discussed.

Symmetropy, an entropy-like measure of visual symmetry

Abstract: A new objective measure of symmetry for single patterns, called symmetropy, is developed on two bases, the two-dimensional discrete Walsh transform of a pattern and the entropy concept in information theory. It is extended to a more general measure, called the symmetropy vector. In order to test the predictive power of the symmetropy vector, multiple regression analyses of judged pattern goodness and of judged pattern complexity were carried out. The analyses show that the symmetropy vector predicts pattern goodness and pattern complexity, as well as the amount of symmetry in a pattern. They also suggest that pattern goodness is a concept based on the holistic properties of a pattern, while pattern complexity (or simplicity) is a concept based on both holistic and partial properties of a pattern.

Method and process for transmitting an image

Abstract: A method and an apparatus for transmitting an image in which the image is sampled at a first plurality of points. The samples are then subjected to a two-dimensional unitary transform to produce a second plurality of transform coefficients, the second plurality being smaller than the first plurality and being obtained either by selection or truncation of the transform to provide the coefficients containing only the lower frequency components of the image. The transform coefficients are transmitted and on receipt converted by the inverse transform to a second plurality of image samples. Suitable transforms include the Hadamard and the discrete cosine. The image transmission is described as part of a viewdata system.

Photoacoustic imaging using the Hadamard transform technique.

Abstract: The principles of Hadamard transformation are applied to photoacoustic imaging. The advantages are twofold: reduction of the power density at the sample, and improvement of SNR due to multiplexing advantage. The compatibility of Hadamard with other multiplex transform techniques is discussed.

On principal submatrices

Abstract: It is shown that if A[ω] is a principal submatrix of the positive definite Hermitian matrix A, then A −1[ω] −(A[ω])−1is a positive semidefinite hermitian matrix. This fact is used to give a brief proof of a result of Saburou Saitoh concerning Hadamard products.

Advantages of Transform Methods in Chemistry

Abstract: Transform techniques offer three main advantages for chemists First, transform techniques provide a variety of simple procedures for manipulating digitized data: smoothing or filtering to enhance signal-to-noise ratio; resolution enhancement (via either narrower line width or more points per line width); changing spectral line shapes (as from Lorentzian to Gaussian); generation of a dispersion spectrum from an absorption spectrum; generation of integrals or derivatives; and clipping to reduce data storage requirements Second, Fourier methods can be used to remove any known irregularities in the excitation waveform, so that the corrected (“deconvoluted”) response reflects only the properties of the sample, and not the effect of the measuring instrument Third, “coded” or “multiplex” detection, followed by Fourier or Hadamard “decoding” can offer a multiplex or Feilgett advantage of up to \(\sqrt N\) in signal-to-noise ratio (or 1/N in time) compared to a scanning instrument, where N is the number of data points in the frequency spectrum

Hadamard and Other Discrete Transforms in Spectroscopy

Abstract: This paper is an introduction to the use of Hadamard and other matrices for increasing the accuracy to which the spectrum of a beam of light can be measured. In the most favorable case if the spectrum has n components the mean squared error in each component is reduced by a factor of n/4. These schemes have the additional merit that the instrumentation required is relatively simple.

Fast cosine transform implementation for television signals

Abstract: An algorithm is described for realisation of the discrete cosine transform. The algorithm has been designed to allow implementation in hardware for 625-line pictures. It employs factorisation of the transform matrix into sparse matrices, some of which are sparse factors of a Hadamard matrix. Further attention is given to the sharing of hardware components so as to reduce circuit complexity.

Orthogonal conversion decoder

Abstract: PURPOSE:To reduce the deterioration of video quality due to an error, by forecasting the sequence value of a received block from a block near the received block according to the pattern expressed by each sequence and replacing the sequence value caused an error with the forecasted value. CONSTITUTION:A coded transmission code according to a transmission line 13 is received and decoded at a transmission decoder 7 to reproduce sequence quantization signals Qi, hi. A quantizer 8 obtains Qi , Qi, hi. The Qi , is the inverse operator to the Qi. The output of the quantizer 8 is inputted to an Hadamard inverter 9 via memories 20, 24, forecast circuits 21, 25, error detection circuits 23, 27, and switching circuits 22, 26. The inverter 9 receives a forecast value alphai (m, n) to a sequence hi (m, n) or a sequence subject to error detection, makes Hadamard inversion and is transmitted from an output terminal 12 as a television signal via a memory 10 and a D/A converter 11.

System for transmitting television picture information using transform coding of subpictures

Abstract: An error protection code which acts on subpictures for the transmission of television picture information. First the picture is subpicture-wise transformed (124) by means of transformation functions, for example, Hadamard functions. Of the coefficients thus formed, a number of most significant coefficient bits which are associated with low frequency transformation functions are protected against a bit error (126). Moreover, a comparatively small number of coefficient bits within said number are protected against an additional bit error.

A Walsh-Hadamard Transform LSI for Speech Recognition

Abstract: Speech recognition systems are coming to a practical stage thanks to the recent progress of the semiconductor technology. We have developed a low cost speaker-dependent speech recognition unit using Walsh-Hadamard transform (WIT). A WHT LSI has been developed to reduce the cost and the space of the recognition unit, and a high rate of recognition has been obtained. The speech recognition algorithm and the LSI are described in this paper.

Asymptotics of hadamard determinants and the convergence of rows of padé approximants for sums of exponentials

Abstract: The asymptotics of Hadamard determinants (of dimension ) for arbitrary fixed and for the function are studied, where are distinct complex numbers with unit modulus. A theorem on the convergence of the th row of the Pade table for the function ( are arbitrary distinct complex numbers) in the topology of holds for arbitrary natural numbers and equal to the number of with modulus that is maximal among the , .Bibliography: 8 titles.

Walsh Spectrum Measurement in Natural, Dyadic, and Sequency Ordering

Abstract: Walsh spectra may have natural, dyadic, or sequency ordering. This paper describes an improved processor design to provide spectra in any selected ordering. The incoming data are stored either directly or in a permuted sequence, and then are followed by a fast Walsh-Hadamard transform. For sequency ordering, the permutation operation is that of a Gray-to- binary code conversion, followed by bit reversal. For dyadic ordering, the operation is only a bit reversal. First a Hadamard processor that uses long shift registers is described. It is adapted to yield coefficients in either of the other two orderings by way of the permuting module (PM).

Performance and computation ranking of fast unitary transforms in applications

Abstract: For several signal processing applications, the usefulness of Fast Unitary Transforms (FUT) is now well recognized [1-7]. For signal representation, filtering and encoding, it is well known that the Karhunen-Loeve (KL) Transform, based on signal statistics, is optimum in various senses, but the KL Transform is slow. Suboptimum FUT's allow a trade-off between performance and speed. In this paper, we compare and rank the KL, Fourier, Walsh-Hadamard, Haar, Discrete Cosine, Slant Walsh Hadamard and Slant Haar Transforms by their performance in applications and by the number of elementary operations they require. In encoding and filtering, recursive techniques are widely used and are generally fast. By considering both performance and computations we are able to compare directly recursive and transform algorithms. The comparison brings to light a performance versus computation bound for the two classes of processing techniques.

System for analyzing complex signals

Abstract: A test system and method for comparatively analyzing complex signals especially those composed of combinations of pulsed signals related to the operational status of apparatus whose operational status is to be determined, is disclosed. In the preferred embodiment a probe, preferably a capacitive probe, is utilized to sense the electric field generated by electrical apparatus. The output signal of the probe is periodically sampled to generate an array of digital signals. This array is processed using Walsh transformations to generate a reference Walsh transform. A second data base is then generated by similarly sampling the electric field generated by an apparatus whose operational status is to be determined. The second data base is then processed to generate a comparison Walsh transform. The operational status of the apparatus whose operational status is to be determined, is then determined by comparing these Walsh transforms.

An efficient, real-time, method for transmitting Walsh-Hadamard transformed pictures

Abstract: This paper presents an efficient method for transmitting regularly-decomposed pictures which have been coded through an orthogonal Walsh-Hadamard transformation. The regular-decomposition procedure converts the picture into a tree representation and compresses the original amount of data by not retaining non-informative areas of the picture. The Walsh-Hadamard transformation is performed on the regularly-decomposed picture as an averaging or smearing process to allow transmission which is more immune to channel errors. It also makes bandwidth reduction possible because, since the image energy which is usually uniformly distributed in the spacial domain now tends to be concentrated near the origin of the transform domain, some of the low-magnitude samples may be discarded. A conceptual design is given where the three steps of regular-decomposition, Walsh-Hadamard transformation, and transmission, instead of being performed sequentially one after the other, are now carried out simultaneously.

Method and apparatus for transmitting an image

Abstract: A method and an apparatus for transmitting an image in which the image is sampled at a first plurality of points. The samples are then subjected to a two-dimensional unitary transform to produce a second plurality of transform coefficients, the second plurality being smaller than the first plurality and being obtained either by selcetion or truncation of the transform to provide the coefficients containing only the lower frequency components of the image. The transform coefficients are transmitted and on receipt converted by the inverse transform to a second plurality of image samples. Suitable transforms include the Hadamard and the discrete cosine. The image transmission is described as part of a viewdata system.

Picture coding in viewdata systems

Abstract: Viewdata systems in commercial use at present offer the facility for transmitting alphanumeric text and graphic displays via the public switched telephone network. An enhancement to the system would be to transmit true video images instead of graphics. Such a system, under development in Britain at present uses Differential Pulse Code Modulation (DPCM) and a transmission rate of 1200 bits/sec. Error protection is achieved by the use of error protection codes, which increases the channel requirement. In this thesis, error detection and correction of DPCM coded video signals without the use of channel error protection is studied. The scheme operates entirely at the receiver by examining the local statistics of the received data to determine the presence of errors. Error correction is then undertaken by interpolation from adjacent correct or previousiy corrected data. DPCM coding of pictures has the inherent disadvantage of a slow build-up of the displayed picture at the receiver and difficulties with image size manipulation. In order to fit the pictorial information into a viewdata page, its size has to be reduced. Unitary transforms, typically the discrete Fourier transform (DFT), the discrete cosine transform (DCT) and the Hadamard transform (HT) enable lowpass filtering and decimation to be carried out in a single operation in the transform domain. Size reductions of different orders are considered and the merits of the DFT, DCT and HT are investigated. With limited channel capacity, it is desirable to remove the redundancy present in the source picture in order to reduce the bit rate. Orthogonal transformation decorrelates the spatial sample distribution and packs most of the image energy in the low order coefficients. This property is exploited in bit-reduction schemes which are adaptive to the local statistics of the different source pictures used. In some cases, bit rates of less than 1.0 bit/pel are achieved with satisfactory received picture quality. Unlike DPCM systems, transform coding has the advantage of being able to display rapidly a picture of low resolution by initial inverse transformation of the low order coefficients only. Picture resolution is then progressively built up as more coefficients are received and decoded. Different sequences of picture update are investigated to find that which achieves the best subjective quality with the fewest possible coefficients transmitted.