A wavelet representation of multivalued images

2004 ◽  
Author(s):  
Paul Scheunders
Keyword(s):  
Wavelet Representation ◽  
Multivalued Images

Characteristic Measures for the Representation of Manufactured Surface Quality

1996 ◽  
Author(s):  
Irem Y. Turner ◽  
R. S. Srinivasan ◽  
Kristin L. Wood
Keyword(s):  
Surface Characterization ◽  
Fourier Spectrum ◽  
Expansion Method ◽  
Design Parameters ◽  
Machining Processes ◽  
Wavelet Representation ◽  
Design And Manufacturing ◽  
Surface Precision ◽  
Signal Characterization ◽  
Generate Characteristic

Abstract In this paper, we investigate four methods that yield mathematical measures to analyze the precision of surfaces of manufactured parts. These four methods, namely the autocorrelation function, the Fourier spectrum, the Karhunen-Loève expansion, and a fractal-wavelet representation, are applied to surfaces produced from grinding processes. The first two methods are standard methods used in the surface analysis literature for qualitative signal characterization. The Karhunen-Loève expansion method, used in various signal processing applications, has never been applied to the field of surface characterization and representation. The fractal-wavelet representation has been previously proposed by the authors; its suitability to generate characteristic measures is investigated in this paper. The existence of characteristic measures of surface precision should aid designers in choosing process and design parameters and in comparing the precision between competing machining processes. The use of such measures is essential in taking a forward step towards integrating the fields of design and manufacturing.

scholarly journals Shannon Wavelets for the Solution of Integrodifferential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Carlo Cattani
Keyword(s):  
Hypergeometric Series ◽  
Sampling Theorem ◽  
Integrodifferential Equations ◽  
Series Connection ◽  
Wavelet Representation ◽  
Connection Coefficients ◽  
Shannon Sampling Theorem ◽  
Shannon Wavelet ◽  
Definition Of ◽  
Shannon Wavelets

Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. Shannon wavelets areC∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).

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