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Classifiers of Digital Modulation Based on the Algorithm of Fast Walsh-Hadamard Transform and Karhunen-Loeve Transform [chapter]

Richterova Marie, Mazalek Antoni
2011 Applications of MATLAB in Science and Engineering  
Karhunen-Loeve transform The Karhunen-Loeve transform (Hua & Liu, 1998 ) (named after Kari Karhunen and Michel Loeve) is a representation of a stochastic process as an infinite linear combination of orthogonal  ...  Performance of the 2-class minimum-distance classifier of FSK based on the WHT www.intechopen.com Classifiers of Digital Modulation Based on the Algorithm of Fast Walsh-Hadamard Transform and Karhunen-Loeve  ...  Classifiers of Digital Modulation Based on the Algorithm of Fast Walsh-Hadamard Transform and Karhunen-Loeve Transform, Applications of MATLAB in Science and Engineering, Prof.  ... 
doi:10.5772/22711 fatcat:rlv3dw5gb5fdfnossv3mucph5y

Page 3976 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Jain, A fast Karhunen- Loéve transform for a class of random processes [IEEE Trans.  ...  Wang [Zhong De Wang], A fast algorithm for the discrete sine transform implemented by the fast cosine transform [IEEE Trans. Acoust. Speech Signal Process. 30 (1982), 814-815] (pp. 94-95); H. B.  ... 

Page 2774 of Mathematical Reviews Vol. , Issue 82f [page]

1982 Mathematical Reviews  
Author’s summary: “For analysis of random processes described by covariance matrices, eigenfunctions of the Karhunen-Loéve basis are optimal.  ...  Solodovnikov, A. I. 82£:94006 Formation of optimal Karhunen-Loeve bases with a fast transform algorithm. (Russian) Voprosy Teor. Sistem Avtomat. Upravlenija No. 5 (1980), 10-27, 153.  ... 

Comparative Study of a Discrete Linear Basis for Image Data Compression

Robert M. Haralick, K. Shanmugam
1974 IEEE Transactions on Systems, Man and Cybernetics  
For a set of thirty-three 64 x 64 images of eleven ditferent categories, we compare the perfo~ of the discrete linear Manuscript transform compression technique with tbe Karhunen-Loeve and Hadamard transform  ...  However, for high compression rates, tbe performance of the discrete transform method is very close to that of the Karbunen-Loeve transform.  ...  Goel of the Center for Research, Inc., University of Kansas, for their help in developing computer programs for implementing the data compression schemes discussed in this paper.  ... 
doi:10.1109/tsmc.1974.5408516 fatcat:xxmb6hw5gzbmhchuapqo6kjika

Discrete Cosine Transform

N. Ahmed, T. Natarajan, K.R. Rao
1974 IEEE transactions on computers  
Andrews, University of Southern California, for his valuable suggestions pertaining to the rate-distortion computation.  ...  Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Lo'eve transform, which is known to be optimal.  ...  TABLE I I MEAN-SQUARE ERROR PEFORMANCE OF VARIOUS TRANSFORMS FOR SCALAR WIENER FILTERING; P = 0.9 M Transform 2 4 8 16 32 64 Karhunen-Loeve 0.3730 0.2915 0.2533 0.2356 0.2268 0.2224 Discrete  ... 
doi:10.1109/t-c.1974.223784 fatcat:grnz5wc5k5hc7bfopaptb65gsy

Spectral Simulation of Functional Time Series [article]

Tomáš Rubín, Victor M. Panaretos
2020 arXiv   pre-print
In the special case of linear processes, we determine the analytical expressions for the spectral density operators of functional autoregressive (fractionally integrated) moving average processes, and  ...  We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators.  ...  of the (inverse) fast Fourier transform.  ... 
arXiv:2007.08458v1 fatcat:yeysdcuoivh75l3vnrnlorsobi

Analysis of Fractals, Image Compression, Entropy Encoding, Karhunen-Loève Transforms

Palle E. T. Jorgensen, Myung-Sin Song
2009 Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications  
The Cuntz relations for a finite set of isometries form a prototype of these relations.  ...  In Karhunen-Loève analysis, we introduce a diagionalization procedure; and we show how the Hilbert space formulation offers a unifying approach; as well as suggesting new results.  ...  The Karhunen-Loève Transform The Karhunen-Loève transform is an operator theoretic tool which has proved effective and versatile in the analysis of stochastic processes (X t ).  ... 
doi:10.1007/s10440-009-9529-y fatcat:urbwzcrdpba53aquqhegrmvp54

Page 1027 of Mathematical Reviews Vol. 55, Issue 3 [page]

1978 Mathematical Reviews  
A fast Karhunen-Loeve transform for a class of random IEEE Trans. Comm. COM-24 (1976), no. 9, 1023-1029. Let {x,} be a first order stationary Gauss-Markov process and let x=(x,, Xa, - ++, Xy).  ...  It is then shown that %, can be computed by a fast Fourier transform algorithm. An extension to two-dimensional processes fi is given.  ... 

Time integration of stochastic generalized equations of motion using SSFEM

Mariusz Poński
2019 Journal of Theoretical and Applied Mechanics  
The methodology is based upon assumption that random fields are from a special class of functions, and can be described as a product of two functions with dependent and independent random variables.  ...  Such an approach allows one to use Karhunen-Loève expansion directly, and the modified stochastic spectral finite element method (SSFEM).  ...  The basic assumption is the simultaneous occurrence of a fast process based on equation (3.21) and a slow process related to equation (3.22) .  ... 
doi:10.15632/jtam-pl.57.1.37 fatcat:skpl4vnmtzamrenurgxbblxkjy

Page 1078 of American Society of Civil Engineers. Collected Journals Vol. 119, Issue 5 [page]

1993 American Society of Civil Engineers. Collected Journals  
The Karhunen-Loeve expansion permits simulation of the realizations of random processes with prescribed spectral description (Kareem and Li 1992).  ...  multivariate random processes.  ... 

Discrete Cosine Transform in JPEG Compression [article]

Jacob John
2021 arXiv   pre-print
This paper discusses the need for Discrete Cosine Transform or DCT in the compression of images in Joint Photographic Experts Group or JPEG file format.  ...  The last section concludes with further real world applications of DCT in image processing.  ...  Figure 1 also shows how close the curve for DCT is to Karhunen-Loève transform.  ... 
arXiv:2102.06968v1 fatcat:ne3yqmqon5flzntbk5ubrueh54

Generalized Wiener Filtering Computation Techniques

W.K. Pratt
1972 IEEE transactions on computers  
In the generalized Wiener filtering process a unitary transformation, such as the discrete Fourier, Hadamard, or Karhunen-Loeve transform is performed on the data that is assumed to be composed of additive  ...  However, by using fast transform algorithms, the computational requirements for some of the transforms, e.g., Fourier and Hadamard, can be reduced significantly.  ...  Messing (42) of the Image Processing Laboratory, University of Southern California, for providing valuable assistance in the experimental portions of this project.  ... 
doi:10.1109/t-c.1972.223567 fatcat:tvrtw5ecijaybcgx2budwmkd5m

Page 2258 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
Author summary: “Suboptimal fast transforms are useful sub- stitutes for the optimal Karhunen-Loéve transform (KLT).  ...  Unser, Michael (CH-LSNP) 86e:94004 On the approximation of the discrete Karhunen- Loéve transform for stationary processes. (French and German summaries) Signal Process. 7 (1984), no. 3, 231-249.  ... 

Karhunen-Loève Expansions for Axially Symmetric Gaussian Processes: Modeling Strategies and L^2 Approximations [article]

Alfredo Alegría, Francisco Cuevas-Pacheco
2020 arXiv   pre-print
First, we investigate a parametric family of Karhunen-Loève coefficients that allows for versatile spatial covariance functions.  ...  In this paper, we focus on Karhunen-Loève expansions of axially symmetric Gaussian processes.  ...  Acknowledgments The research work of Alfredo Alegría was partially supported by Grant FONDECYT 11190686 from the Chilean government.  ... 
arXiv:2007.01961v1 fatcat:ain5sevaija7jk3rlkcoobefpm

Page 1381 of Mathematical Reviews Vol. 56, Issue 4 [page]

1978 Mathematical Reviews  
For the special case of independent signalling random processes, the results for continuous data are similar to those obtained by Fralick for discrete, conditionally independent data.  ...  Authors’ summary: “After surveying existing feature selection procedures based upon the Karhunen-Loéve (K-L) expansion, the paper describes a new K-L technique that overcomes some of the limitations of  ... 
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