On the estimation of wavelet coefficients

In wavelet representations, the magnitude of the wavelet coefficients depends on both the smoothness of the represented function f and on the wavelet. We investigate the extreme values of wavelet coefficients for the standard function spaces A_k=f| ∥f^k)∥₂ ≤ 1}, k∈N. In particular, we compare two important families of wavelets in this respect, the orthonormal Daubechies wavelets and the semiorthogonal spline wavelets. Deriving the precise asymptotic values in both cases, we show that the spline constants are considerably smaller. This revised version was published online in June 2006 with corrections to the Cover Date.     

System identification based on distribution theory and wavelet transform

A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.     

Orthogonal and Nonorthogonal Multiresolution Analysis, Scale Discrete and Exact Fully Discrete Wavelet Transform on the Sphere

Based on a new definition of dilation a scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen. In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully discrete wavelet approximation is discussed in the case of band-limited wavelets. June 18, 1996. Date revised: January 14, 1997.