Good fitting of traffic data is important to traffic study because initial and boundary conditions of dynamic traffic models and relationships among traffic variables are dependent on the calibration of data. In this paper, a denoising method of traffic data, such as speed, density and flow, is proposed and discussed numerically. The denoising procedure is based on Daubechies wavelet transform ...

This letter addresses two issues in clock synchronization in the context of the theory of wavelets: design of prefilters eliminating pattern-dependent jitter (PDJ) and design of lowjitter shaping pulses for timing recovery. We derive low-jitter symmetric and time-limited shaping pulses via a perturbational technique from the autocorrelation of the Daubechies scaling function.

Wavelets have become a popular topic, especially in their use for image compression. Many papers have been written, but most are oriented toward mathematicians. This paper will present an application of the Daubechies wavelet for image compression with emphasis on the implementation and not on the mathematical analysis.

For signal-based design of orthonormal (ON) wavelets, an optimization of a cost function over an N -dimensional angle space is required. However: (1) the N -dim space includes both smooth and non-smooth wavelets; (2) many of the smooth wavelets are similar in shape. A more practical approach for some applications may be to construct a library of smooth ON wavelets in advance—a library that cons...

This paper explores the Sobolev regularity of rank M wavelets and reenement schemes. We nd that the regularity of orthogonal wavelets with maximal vanishing moments grows at most logarithmically with lter length when M is odd, but linearly for even M. When M = 3 and M = 4, we show that the regularity does achieve these upper bounds for asymptotic growth, complementing earlier results for M = 2....

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets | that is, the design of minimal length wavelet lters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and two distinct wavelets. Having more wavelets than necessary gives ...

We generalize earlier results concerning an asymptotic error expansion of wavelet approximations. The properties of the monowavelets, which are the building blocks for the error expansion, are studied in more detail, and connections between spline wavelets and Euler and Bernoulli polynomials are pointed out. The expansion is used to compare the error for different wavelet families. We prove tha...

Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments. The increased regularity is obtained by optimizing the locations of the roots the scaling filter has on the interval (π/2, π). The results improve those obtai...

We investigate the description of statistical field theories using Daubechies’ orthonormal compact wavelets on a lattice. A simple variational approach is used to extend mean field theory and make predictions for the fluctuation strengths of wavelet coefficients and thus for the correlation function. The results are compared to Monte Carlo simulations. We find that wavelets provide a reasonable...

Wavelet networks are a class of neural network that take advantage of good localization properties of multi-resolution analysis and combine them with the approximation abilities of neural networks. This kind of networks uses wavelets as activation functions in the hidden layer and a type of back-propagation algorithm is used for its learning. However, the training procedure used for wavelet net...