Showing papers on "Hadamard transform published in 1984"

Coding of Real-Number Sequences for Error Correction: A Digital Signal Processing Problem

Abstract: Error-correcting codes defined over the real-number and complex-number fields are introduced. The possibility of utilizing realnumber arithmetic permits the codes to be implemented with operations normally available in standard programmable digital signal processors by methods which are discussed. Hadamard and discrete Fourier transform codes are presented for block coding, and the latter are seen to be cyclic and to include the class of BCH codes. It is shown that maximum distance separable real-number BCH ( N, K ) codes exist for all nontrivial values of N and K . A large class of block and convolutional real-number single-error-correcting codes, derived from similar codes over GF(p) , are presented. Both block and convolutional codes are seen to be describable by the z -transform in a manner which emphasizes their similarities to conventional digital signal processing structures such as digital filters and digital filter banks. Methods for correcting weight t and t + 1 errors in a t error-correcting code are demonstrated and interpreted; in particular, the use of a VLSI digital signal processor for implementation of an algorithm for correcting almost all double adjacent error patterns in a single-error-correcting convolutional code is discussed.

Image processing method using a collapsed walsh-hadamard transform

Abstract: An improved image processing method uses a modified Walsh-Hadamard transform to remove noise and preserve image structure in a sampled image. Image signals representative of the light value of elements of the image are grouped into signal arrays corresponding to blocks of image elements. These signals are mapped into larger signal arrays such that one or more image signals appear two or more times in each larger array. The larger arrays are transformed by Walsh-Hadamard combinations characteristic of the larger array into sets of coefficient signals. Noise is reduced by modifying--i.e., coring or clipping--and inverting selected coefficient signals so as to recover processed signals--less noise--representative of each smaller signal array. The results exhibit acceptable rendition of low contrast detail while at the same time reducing certain processing artifacts characteristic of the unimproved Walsh-Hadamard block transform.

Transformation circuit for implementing a collapsed walsh hadamard transform

Abstract: A unit transformation circuit transforms three discrete input signals into a set of transform coefficient signals characteristic of a "collapsed" Walsh-Hadamard transform. The unit transformation circuit includes two tiers of arithmetic networks. In the first tier, a pair of arithmetic networks (36, 38) generates A) first sum and difference signals from the first and second input signals and B) second sum and difference signals from the second and third input signals. Arithmetic networks (40, 42) in the second tier generate a set of coefficient signals from A) the sum of the first and second sum signals B) the sum of the first and second difference signals and C) the difference between the first and second difference signals. The unit transformation circuit forms a fundamental circuit element from which more complex circuits are constructed capable of transforming larger numbers of discrete input signals.

Symmetric Hadamard series

Abstract: In a general curved space–time, the requirements that the Feynman Green’s function be symmetric and have the Hadamard form are shown to result in specific constraints on the local behavior of the function. These constraints are solved yielding a general form for the function.

How good is Hadamard's inequality for determinants?

Abstract: Let A be a real n × n matrix and define the Hadamard ratio h(A) to be the absolute value of det A divided by the product of the Euclidean norms of the columns of A. It is shown that if A is a random variable whose distribution satisfies some simple symmetry properties then the random variable log h(A) has mean and variance . In particular, for each e > 0, the probability that h(A) lies in the range tends to 1 as n tends to ∞.

Fast progressive reconstruction of a transformed image (Corresp.)

Abstract: Fast methods for performing progressive reconstruction of Fourier and Hadamard transformed images have been developed Reconstruction of an N \times N point transformed image can be evaluated in order N^{2} \log_{2} N instructions Accumulation of round-off errors due to iteration is reduced by the factor (\log_{2} N + 1) / N^{2} , compared with direct evaluation of the inverse transform

Improving Hadamard's inequality *

Abstract: We study several bounds for the determinant of an n × n positive definite Hermitian matrix A. These bounds are the best possible given certain data about A. We find the best bounds in the cases that we are given: (i) the diagonal elements of A: (ii) the traces trA,tr A 2 and n and (iii)n, tr A tr A 2 and the diagonal elements of A. In case (i) we get the well known Hadamard inequality. The other bounds are Hadamard type bounds. The bounds are found using optimization techniques.

A new image coding technique using transforms vector quantization

Abstract: A new interframe coding technique is proposed. Where a two-dimensional Hadamard transform is applied on each sub-block of successive frames, and an adaptive vector quantisation scheme is applied along the transformed blocks of the successive frames. The performance of the algorithm is evaluated by computer simulation on sequence of moving images.

Video compression system

Abstract: Video compression is achieved by taking the Hadamard transform of video data, comparing Hadamard coefficients from consecutive lines, encoding the changed coefficient values via an entropy coding technique, removing superfluous bits and storing the data on a magnetic tape. The stored data can then be reproduced, unpacked and decoded to regenerate the original video data signals, thereby achieving a very high degree of compression with little or no degradation of image quality.

Walsh-transform coding of the speech residual in RELP coders

Abstract: A method is described for encoding the residual speech signal in residual-excited linear predictive coders. In this method, a low-sequency baseband of the residual is transmitted by encoding the coefficients of the lower half of the Walsh spectrum. Techniques for reconstructing the upper portion of the spectrum are discussed. The resulting algorithms are simple to implement and simulation studies have shown that a bit rate of 10 kbits-1 can be achieved.

The Walsh-Hadamard transform: an alternative means of obtaining phase and amplitude maps.

Abstract: Currently, Fourier analysis is a method for obtaining the phase and amplitude images used to evaluate abnormalities of cardiac contraction. Since this technique is time-consuming, the present work investigates the application of another algorithm used in digital signal processing: the Walsh- Hadamard transform ( WHT ). This method provides a 48% time saving because it requires only elementary algebraic operations. The study presents the results obtained processing 30 blood-pool cardiac acquisitions in various diseases. No significant difference was found in the pairs of maps and in the parameters chosen for comparison of the data.

Relations between Certain Sums and Integrals Concerning Power Series with Hadamard Gaps

Abstract: Let ∑ kakznλ be analytic for . It is shown that if f has Hadamard gaps , i.e. then the finiteness of essentially equivalent to that of where R is a radius of . More precisely, the sum is finite if the integral is, even for an arbitrary curve instead of a radius with no condition whatever on α. For the other direction the restriction α> –1 is necessary.

Nonisomorphic complete sets of orthogonal f-squares and hadamard matrices

Abstract: Five nonisomorphic classes of Hadamard matrices of order 16 were given by Hall (1961). Three of these Hadamard classes have a 4 ×4 row and column structure; they generate three nonisomorphic complete sets of nine orthogonal F(4;2,2)-squares, one of which shows a previously unreported pattern. The remaining two Hadamard classes do not produce complete sets of F-squares, Each of the five Hadamard classes corresponds to a distinct set of single-degree-of-freedom contrasts in an analysis of variance.

Object Restoration by Zero Location

Abstract: The relationship between the location of zeros of scattered fields and the corresponding object information in one dimension is investigated using the theory of entire functions. Each zero of a Hadamard factor in the scattered field is shown to contribute a complex harmonic in the object space. Using this formalism, we investigate how noise in the scattered field and data confined to a spectrum of finite extent affect object reconstruction and show that this inverse process is unstable. We indicate how the task of input restoration can be regularized by introducing a global parametrization containing a modulus bound and expressing the total energy of the object wave in terms of the zero configuration in the scattered field. This leads to object reconstruction by solving a set of nonlinear algebraic equations. The method is illustrated with a computer simulation of a practical example.

On Designs Constructed from Hadamard Matrices

Abstract: Soit H 1 (μ) des configurations (1-(4μ,2μ,2μ) affines dont les duales sont aussi affines. On demontre que si une matrice de Hadamard d'ordre μ existe, alors le nombre de classes d'equivalences de matrices de Hadamard d'ordre μ2 n est au moins n−1

Decoding system of picture signal

Abstract: PURPOSE:To decode combined codes of each sequence, by converting input signals to a parallel signal, and performing inversion of linear forecasting for the sequence transmitted as a forecasted error and applying Hadamard's inversion, and thereby obtaining a reproduced picture element signal. CONSTITUTION:Picture element signals x1-x4 read out by scanning lines are inputted to a Hadamard's converter 10, and sequences H0a-H3a converted in frequency domain are added to a quantizing section 20. Out of sequence quantized values H0-H3 from the quantizing section 20, sequence quantized values H0, H2 transmitted as forecasted errors are added to a forecasting device 30, and an error quantized value DELTAH0 is added to a comparator 41 of a variable length coding circuit PLA. The combination number C0-C4 of the sequence is discriminated by the comparator 41, and added to ROM42 as an address. A called code length CL and block code BC are set to a counter 43 and a shift register 45. Inversion of linear forecasting is performed, and combined codes are decoded by Hadamard's inversion.

Automated identification of rock boundaries; an application of the Walsh transform to geophysical well-log analysis; discussion

Abstract: Lanning and Johnson’s paper presents the technique of Walsh transform domain low‐pass filtering as a means of enhancing transitions in well logs prior to boundary picking. They argue that existing fast means of computing the Walsh transform (fast Walsh transform algorithms) make this procedure particularly efficient. In this discussion it is shown that, for all practical cases of interest, the results of their paper can be obtained without any mention of the Walsh transform. In fact, using the Walsh transform unnecessarily increases computational complexity. Specifically, it is shown that the low‐pass sequency filtering described for obtaining a stepped version of the original signal with a given step width is equivalent to segmenting simply the signal into equal length segments and replacing all values in each segment by the segment average.

A deblurring algorithm using edge gradient for the Walsh-Hadamard transform image coding system

Abstract: This paper describes a transform gradient combination scheme for deblurring pictures in band compression systems. Algorithms are presented for reconstruction at the receiver. An experiment has been conducted using a digitized image and the quality of the reproduced picture has been measured in terms of percentage m.s.e., probability of high errors, and number of missed and false edges.

Coding system of picture signal

Abstract: PURPOSE:To ensure the variable length coding with high efficiency, by combining the quantized values of sequences obtained by dividing an input picture with a Hadamard conversion. CONSTITUTION:Picture element signals x1-x4 are supplied to a Hadamard converter 10, and sequences H0a-H3a converted into frequency regions are supplied to an quantizing part 20. Quantizers 22, 23 and 24 deliver the sequence quantized value H2 of horizontal component, the sequence quantized value H1 of vertical component and the sequence quantized value H3 of slope component respectively. An estimator 30 performs a linear estimation to the sequence H0 of DC component and delivers an estimation error component DELTAH0. A comparator 41 consists of a PLA and designates the address of an ROM42 based on sequence quantized values H0, H1, H2 and H3. A code length data CL is read out of the ROM42 and then set to a counter 43. The contents of shift registers 44 and 45 are delivered in response to the count value of the counter 43.

Performance of Transform Coding for Carrier Chrominance Signals

Abstract: This paper describes the results of theoretical studies made on performance of various kinds of intrafield two-dimensional transform codings (Hadamard, cosine, and slant) for carrier chrominance signals, by introducing a new measure (transform coefficients of zero variance) for such coding performances. In addition, a comparative study of the performance of these transform codings is performed for different sampling frequencies (2f_{sc}, 3f_{sc}, 4f_{sc}) with the same transmission rate, taking into account the tradeoff between the number of bits assigned to a picture element at each sampling frequency and the autocorrelation between adjacent picture elements.

Second Order Corrected Hadamard Formulae

Abstract: The second order correction to the Hadamard formulae for the Green function, harmonic measures and period matrix of a two-dimensional domain is obtained iu the context of the domain variational theory. Die Hadmard-Formel mit Korrekturen der zweiten Ordnung Die Korrekturen der zweiten Ordnung zur Hadamard Formel fur die Greensche Funktion, harmonische Mase und die Perioden-Matrix eines zweidimensionalen Bereichs werden berechnet im Rahmen der Theorie der Variation des Definitionsbereichs.

Ring type single photon ect device

Abstract: PURPOSE:To obtain different tomographic images without increasing the number of detector layers, by arranging a Hadamard mask on the radiant rays incidence side of each radiant rays detector, and reconstituting plural tomographic images at different positions at one-slot intervals of Hadamard masks. CONSTITUTION:Each radiant rays detector consists of a scintillator 11, light guide 12, and a photomultiplier 13. Many radiant rays detectors are arranged annularly in a ring type radiant rays detector array and Hadamard masks 14 serving as collimators are arranged inside of the array, i.e. on radiant rays incidence sides of scintillators 11. Those Hadamard masks 14 are moved, slot by slot, by one slot at right angles to tomographic images and a cyclic Hadamard matrix corresponding to the array order of the opening parts and shield parts of the Hadamard masks 14 is made to operate on detector outputs obtained at respective positions and also standardized to obtain data.