scholarly journals Reversible Hadamard transforms

2007 ◽  
Vol 20 (3) ◽  
pp. 309-330 ◽  
Author(s):  
Hakob Sarukhanyan ◽  
Sos Agaian ◽  
Karen Egiazarian ◽  
Jaakko Astola
Keyword(s):  
Digital Image ◽  
Input Signal ◽  
Higher Order ◽  
Transform Coding ◽  
Hadamard Transform ◽  
Fast Transform ◽  
Coding Method ◽  
Block Transform ◽  
Hadamard Transforms

A coding method which reconstruct an original digital image without distortion is called "reversible coding". In case of the classical block transform coding (Cosine, Hadamard, Haar and etc) we have to make the number of levels of the transform coefficient very large in order to reconstruct the input signal with no distortion. In this paper we propose reversible Hadamard transform matrices. We give a recursion methods for generation of various type of real and complex reversible Hadamard transform matrices of higher order and corresponding fast transform algorithms.

scholarly journals Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

2020 ◽  
pp. 237-249
Author(s):  
L. V Stepanova
Keyword(s):  
Series Expansion ◽  
Digital Image ◽  
Power Series Expansion ◽  
Crack Tip ◽  
Higher Order ◽  
Accurate Estimation ◽  
Principal Stresses ◽  
Isochromatic Fringe ◽  
Higher Order Terms ◽  
Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

scholarly journals Simple Speech Transform Coding Scheme using Forward Adaptive Quantization for Discrete Input Signal

2019 ◽  
Vol 48 (3) ◽  
pp. 454-463
Author(s):  
Zoran Peric ◽  
Milan Tancic ◽  
Nikola Simic ◽  
Vladimir Despotovic
Keyword(s):  
Input Signal ◽  
System Performance ◽  
Signal Reconstruction ◽  
Objective Measure ◽  
Performance Estimation ◽  
Quantization Noise ◽  
Transform Coding ◽  
Coding Scheme ◽  
First Case ◽  
Adaptive Quantization

We propose a speech coding scheme based on the simple transform coding and forward adaptive quantization for discrete input signal processing in this paper. The quasi-logarithmic quantizer is applied to discretization of continuous input signal, i.e. for preparing discrete input. The application of forward adaptation based on the input signal variance provides more efficient bandwidth usage, whereas utilization of transform coding provides sub-sequences with more predictable signal characteristics that ensure higher quality of signal reconstruction at the receiving end. In order to provide additional compression, transform coding precedes adaptive quantization. As an objective measure of system performance we use signal-to-quantization-noise ratio. Sysem performance is discussed for two typical cases. In the first case, we consider that the information about continuous signal variance is available whereas the second case considers system performance estimation when we know only the information about discretized signal variance which means that there is a loss of input signal information. The main goal of such performance estimation comparison of the proposed speech signal coding model is to explore what is the objectivity of performance if we do not have information about a continuous source, which is a common phenomenon in digital systems.

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