A QUICK GLANCE OF SPLINE WAVELETS AND ITS APPLICATIONS

B Kunwar, V.K Singh, Kanchan Lata Gupta

Abstract: Polynomial spline wavelets have played a momentous role in the enlargement of wavelet theory. Due to their attractive properties compact support, good smoothness property, interpolation property, they are now provide powerful tools for many scientific and practical problems. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. This paper is a summary of spline wavelet which started with splines and ends with the applications of spline wavelets. The paper is divided into four sections. The first section contains a brief introduction of splines and the second section is devoted to the discussion of spline wavelet construction via multiresolution analysis (MRA) with emphasis on B-spline wavelet. The underlying scaling functions are B-splines, which are shortest and most regular scaling function. In the third section, some remarkable properties of spline wavelets are discussed. The orthogonality and finite support properties make the spline wavelets useful for numerical applications and also have the best approximation properties among all the known wavelets. And the last section enclose a brief discussion of application of spline wavelets.ax

Keywords: Splines, Multiresolution Analysis, Semi-Orthogonal Bases, Compact Support.

DOI: https://doi.org/10.15623/ijret.2016.0510009