Showing papers on "Hadamard transform published in 1985"

Hadamard matrices and their applications

Abstract: Construction of classic Hadamard matrices.- Construction of generalized Hadamard matrices.- Application of Hadamard matrices.

Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation.

Abstract: Experimental results are presented demonstrating that humans can make effective use of prior knowledge for detecting and identifying visual signals in static noise. The signals were selected from an orthogonal Hadamard set. There was a marked drop in detection performance when observers did not know which signal was present. The drop was in excellent quantitative agreement with that predicted by the theory of signal detectability. The statistical efficiency of the human observers was 33% in both cases (detection with and without prior knowledge). When interpreted in terms of channel uncertainty, the detection results demonstrated an upper limit of 10 orthogonal, uncertain channels. The statistical efficiency for the Hadamard signal-identification task was 40%. All the results are consistent with the standard theory of signal detectability based on a Bayesian maximum a posteriori probability decision strategy using cross correlation (or matched filtering) of expected signal profiles with those present in the display.

Hadamard graphs. II

Abstract: In order to provide an algebraic graph theoretic background for Hadamard matrices and designs Hadamard graphs are introduced and their spectra are determined.

Open mappings theorems and linearization stability

Abstract: An important computation rule for tangent cones is examined. Two results are given which assume only Hadamard differentiability (and a variant of it) instead of strict Frechet differentiability. This allows the consideration of concrete examples such as superposition operators and can be applied to the problem of linearizing a nonlinear equation or inequality.

Spectral filtering using the fast Walsh transform

Abstract: This paper describes a method of doing spectral filtering using the fast Walsh transform (FWT) rather than the fast Fourier transform (FFT). Rather than using the Walsh transform to find Fourier coefficients which can then be filtered by ordinary means, as was done in [2], we find a new filter function, expressed as a matrix, that does the same filtering operation in the Walsh domain as the filter function matrix in the Fourier domain. This new filter matrix, called the Walsh gain matrix (G w ), is block-diagonal and real while the Fourier gain matrix (G f ) is complex diagonal. The block-diagonal structure of G w and a condition that causes G w to be real are proven. An off-line method for finding G w given G f is presented. Using the block-diagonal structure of G w it is proven that spectral filtering via FWT requires fewer multiplications than spectral filtering via FFT for N \leq 64 where N is the length of the sequence of samples of the input signal (N is a power of 2). A special condition on G f gives a G w such that spectral filtering via FWT becomes better, in terms of multiplications, than spectral filtering via FFT for N \leq 128 .

System for decoding and displaying encoded television pictures

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.

Hankel-Hadamard analysis of quantum potential x2+λx2/(1+gx2)

Abstract: The Hankel-Hadamard moment determinant analysis of Handy and Bessis (1985) is applied to the potential x2+ lambda x2/(1+gx2). Rapidly convergent lower and upper bounds to the ground-state energy and first excited state are obtained. Application of a novel type of Pade analysis allows the determination of all other excited states through an orthogonality quantisation prescription.

Quantum states and the Hadamard form. III. Constraints in cosmological space-times.

Abstract: We examine the constraints on the construction of Fock spaces for scalar fields in spatially flat Robertson-Walker space-times imposed by requiring that the vacuum state of the theory have a two-point function possessing the Hadamard singularity structure required by standard renormalization theory. It is shown that any such vacuum state must be a second-order adiabatic vacuum. We discuss the global requirements on the two-point function for it to possess the Hadamard form at all times if it possesses it at one time.

A fast matrix quantizer for image encoding

Abstract: This paper discusses a multi-stage matrix quantizer with a tree structure for image encoding wherein the number of searches required is a linear function of the product of the matrix size and the bit rate rather than an exponential one as in the case of a full search encoder. A two-step nine-way classification procedure is employed in order to preserve the edge contents of images. Further data rate reduction is achieved by preprocessing the images with a simple linear Hadamard transformer. A kl subblock of the input image is classified nine ways to detect the edge orientation. If it is not an edge a shade codebook is designed. Eight different codebooks are generated to accommodate each of the edge orientations under consideration. It is observed that the staircase degradation due to quantization is greatly reduced when edge detection is used. It is also found that the degradation due to tree encoding is only about 0.5 dB as compared to full search encoding.

Construction of Orthogonal Main-Effect Plans Using Hadamard Matrices

Abstract: Some systematic methods for constructing orthogonal main-effect plans, using Kronecker and other products of Hadamard matrices, are introduced. These are generalizations of the methods suggested earlier by Margolin and Dey and his co-workers. Two series of plans of the type t.2 t(n − 1) and 4 t − 1.2 n are constructed. The first series is saturated and the second is saturated for t = 4. In addition to generating previously reported plans, the proposed methodology provides many new plans.

On the hadamard products of Schlicht functions and applications

Abstract: We show that each of the schlicht classes of starlike, convex, close-to-convex and strongly starlike with respect to symmetric points is invariant under the Hadamard product with the class of convex functions. The influence of certain operators over these classes is also investigated.

Second‐order corrected Hadamard formulas

Abstract: The second‐order correction to the Hadamard formulas for the Green’s function, harmonic measures, and period matrix of a two‐dimensional domain is obtained in the context of the domain‐variational theory.

Statistical design of analysis/Synthesis systems with quantization

Abstract: A statistical model is used for the optimal design of analysis/synthesis systems which include quantization of the signals in the separate bands. Two error measures are used. One is a generalization of the usual statistical mean square error (MSE) to time-varying systems (since analysis/synthesis systems with decimation and interpolation are time varying). The second measure is the time average of the expected l 2 distance between the output of the analysis stage and the analyzed reconstructed signal. The proposed design methods are based on minimizing these error measures and shown to apply not only with the DFT but also with any linear regular transform (e.g. Hadamard, DCT). The above two error measures are shown to be equivalent for a wide class of transforms (including the DFT). The design methods is applicable to either finding an optimal synthesis window for a given analysis window, or finding an optimal analysis window for a given synthesis window. The optimal windows (filters) are obtained by solving a set of linear equations. An optimal analysis/synthesis system is obtained using an iterative algorithm which is based on alternately solving these two sets of linear equations. When no quantization is applied the new design methods coincides with previously reported methods.

Construction of Orthogonal Main-Effect Plans

Abstract: Some systematic methods for constructing orthogonal main-effect plans, using Kronecker and other products of Hadamard matrices, are introduced. These are generalizations of the methods suggested earlier by Margolin and Dey and his co-workers. Two series of plans of the type t.2t(n 1) and 4'-1.2" are constructed. The first series is saturated and the second is saturated for t = 4. In addition to generating previously reported plans, the proposed methodology provides many new plans.

The Variation of Characteristic Values and Functions

Abstract: The Green’s function associated with the second order equation $$ u'' + q(x)u = 0, u (a) = u (1) = 0, $$ (1) has been discussed Analogous methods are used in the following chapter to obtain the Hadamard variational formula

Panel-Discussion on Two Dimensional Signals and Codes

Abstract: It is hard to imagine any problem that does not have some two-dimensional (2D) aspects. When you draw a graph with a horizontal axis and a vertical axis, that is 2D, if you write things out on a page, that page is 2D. Let me first quote the abstract which I prepared for this panel discussion. You will see there what came to my mind in the communications areas which have clear 2D features: ‘Finding good frequency-hop patterns is an example of 2D signal design in time and frequency. Applications of these signals include: frequency hopping for spread-spectrum communications to achieve either anti-jamming (A-J) or lew probability of intercept (LPI), or for frequency diversity, or for multiple-access, and frequency-hop signals for radar, sonar, and 2D synchronisation. The transmission of pictorial data provides another natural context for 2D signal design. A variety of transforms (e.g., 2D Fast Fourier transforms, Hadamard transforms, etc.) are used to encode such data. Inverse problems of creating accurate 2D and even 3D reconstructions of surfaces from electromagnetic wavefronts arise in contexts as diverse as radar mapping of planetary surfaces and computer-aided X-ray tomography (‘CAT-scans’)’.

The Hadamard Variational Formula

Abstract: In an earlier chapter, the functional equation technique of dynamic programming was applied to obtain a variational equation for a Green’s function corresponding to a second order ordinary differential equation. In the present chapter, this method is extended to apply to elliptic partial differential operators, and a first consequence is the classical Hadamard variational formula.

Hadamard transform seperation of NTSC component signals

Abstract: The transmission of NTSC composite color images over digital communication channels is generally accomplished by coding the less correlated component signal, YIQ. Unless the video source is available, the component signals are separated from the composite signal by using comb-filters. Comb-filtering is generally performed in the temporal domain. This paper shows that by properly sampling the NTSC composite color signal at four times the color subcarrier, the Walsh-Hadamard transform acts like a comb filter and separates the YIQ components of the composite signal. The YIQ components will be mapped into specific locations of the coefficient matrix.