We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of th...

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated to Legendre multiresolution analysis is ...

in this paper a new optical channel drop filter (cdf) based on two dimensional (2-d) photonic crystals (phc) with hexagonal shaped structure is proposed and numerically demonstrated by using the finite-difference-time-domain (fdtd) and plane-wave-expansion (pwe) techniques. photonic crystals (phcs) are artificial dielectric nanostructure materials in which a periodic modulation of the material ...

We use similarities with people we know already as a means to enhance the speaker verification accuracy. Motivated by this, we use cosine distance similarities with a set of reference speakers, cosine distance features (CDF), to improve the performance of speaker verification systems for clean and additive noise test conditions. We used mel frequency cepstral coefficients, power normalized ceps...

ÐWe present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients ar...

The wavelet transform (in the signal processing context) is a method to decompose an input signal of interest into a set of elementary waveforms, called “wavelets,” and provides a way to analyze the signal by examining the coefficients (or weights) of these wavelets. The Fourier transform also decomposes signals into elementary waveforms; however, in this case, they are global oscillations, i.e...

The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is compu...

We construct orthonormal wavelet bases of L2(IR) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H2 of all two-dimensional (2D) scaling coefficients satisfying the orthogonality condition as an implicit function. This set includes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H2 at HN , the scaling coefficients...