This paper deals with the wavelet-based performance analysis of the safety barrier for use in a full-scale test. The test involves a vehicle, a Ford Fiesta, which strikes the safety barrier at a prescribed angle and speed. The vehicle speed before the collision was measured. Vehicle accelerations in three directions at the centre of gravity were measured during the collision. The yaw rate was m...

We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polyno-mials are parametrized by the circle, and we compute that the corresponding filters generate irreducible mutually disjoint representations of of the Cuntz algebra O 2 except at two...

Image compression is the important task for the medical images. Economic and effective image compression techniques are hardly required to minimize the storage volume of medical database in hospitals as well as maintaining the image quality. But the transmission and storage of such a large data could be a tedious job. There are various methods to encrypt the images while transmission. In this r...

1. The unit sphere in R and the classification of regular solids 1 2. Symmetries of platonic solids 3 3. Basic representation theory of finite groups 6 4. Haar basis of L(R) 17 5. Haar multiresolution of L(R) 20 6. Daubechies wavelets 22 7. Wavelets and group representations 24 8. Numerical integration on the sphere 25 9. Unique factorization domains and Hilbert’s Nulstellensatz 27 10. Spherica...

We exhibit the necessary range for which functions in Sobolev spaces L p s $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such Battle–Lemarié wavelets. also consider natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work Seeger Ullrich, where analogous results were established Haar system.

This paper analyses the application of wavelets for the efficient detection of QRS complex in ECG. Wavelets provide simultaneous time and frequency information. In this research, the effects of the properties of different wavelet functions, such as time/frequency localization and linearity, on the accuracy of QRS detection are examined. Initially, a wavelet transform filtering is applied to the...

Wavelets are mathematical tools for hierarchically decomposing functions. Wavelet Transform has been proved to be a very useful tool for image processing in recent years. It allows a function which may be described in terms of a coarse overall shape, plus details that range from broad to narrow. The most distinctive feature of Haar Transform lies in the fact that it lends itself easily to simpl...

Abstract. In the paper, a new original procedure for the evaluation of discrete Haar spectra for separate fragments (blocks) of a digital image is proposed. The procedure explores specific properties of Haar wavelets, refers to the assumption that Haar spectrum of the whole image is known, and is much faster than direct evaluation of Haar spectral coefficients for the respective image blocks. I...

A Haar wavelet collocation method (HWCM) is presented for the solution of Riccati equation subject to two-point and integral boundary condition. The qua?silinearization technique applied linearized then with condition solved by converting into system algebraic help wavelets. We have considered three different form Reccati equation, two having one numerical results obtained HWCM are stable, effi...

There is an apparent renewed interest in application of the Haar wavelet transform in switching theory and logic design.1–6 In particular, the discrete Haar transform appears very interesting for its wavelets-like properties and fast calculation algorithms. The applications have been found in circuit synthesis, verification and testing.1–9 For applications of the Haar transform in logic design,...