In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C1 and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is antisymmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of non-linear Hunter–Saxton equation. Firstly, operational matrices integration associated with are constructed by following strategy Chen Hsiao. The merged used to convert given problem into system algebraic equations that can be solved any classical method, such as Newt...

Abstract We revisit the construction of wavelets on interval with various degrees polynomial exactness, and explain how existing schemes for orthogonal- Spline can be extended to compactly supported delay-normalized wavelets. The contribution differs substantially from previous ones in results are stated deduced: linear algebra notation is exploited more heavily, use sums complicated index redu...

Ruttimann et al. have proposed to use the wavelet transform for the detection and localization of activation patterns in functional magnetic resonance imaging (fMRI). Their main idea was to apply a statistical test in the wavelet domain to detect the coefficients that are significantly different from zero. Here, we improve the original method in the case of non-stationary Gaussian noise by repl...