Abstract—Recently, in [7] wavelets have been constructed by taking trigonometric B-splines as the scaling functions. In this paper, we study some of its qualitative properties like decay, regularity and vanishing moments. In particular, we show that if the order of the scaling function is n then these wavelets have n-vanishing moments, have regularity of order more than n-1 and decay to zero very fast like inverse of a polynomial.

Index Terms—Trigonometric b-spline, wavelet, decay, regularity, vanishing moments.

M. K. Jena is with the Department of Mathematics, VSS University of Technology, Odisha, Burla-768018, India (e-mail: maheny2010@yahoo.com, maheny2010@gmail.com).

Cite: Mahendra Kumar Jena, "Qualitative Properties of Wavelets Constructed from Trigonometric B-Splines," International Journal of Applied Physics and Mathematics  vol. 2, no. 4, pp.  231-233, 2012.