Tight wavelet frames generated by three symmetric B-spline functions with high vanishing moments

• Published in: Proceedings of the American Mathematical Society Vol. 132; no. 1; pp. 77 - 86
• Main Authors: Han, Bin, Mo, Qun
• Format: Journal Article
• Language: English
• Published: Providence, RI American Mathematical Society 01-01-2004
• Subjects: Approximations and expansions; Exact sciences and technology; Fourier analysis; Harmonics; Increasing functions; Integers; Mathematical analysis; Mathematical functions; Mathematical moments; Mathematics; Numbers; Polynomials; Sciences and techniques of general use; Sine function; vanishing moments; B$-spline functions; Symmetric tight wavelet frames; B spline; Shift; Frame; Vanishing moment; Approximation; Support; Statistical moment; Symmetric function; N order; Spline; Integer; Wavelets; Symmetric tight wavelet frame; Mathematical analysis; Real function; B spline function
• ISSN: 0002-9939; 1088-6826
• DOI: 10.1090/S0002-9939-03-07205-8

In this note, we show that one can derive from any B-spline function of order m (m\in \mathbb N) an MRA tight wavelet frame in L_2(\mathbb R) that is generated by the dyadic dilates and integer shifts of three compactly supported real-valued symmetric wavelet functions with vanishing moments of the highest possible order m.