Let G = ( R∗+ × SO0(1, n) ) n Rn+1 be the Weyl-Poincaré group and KAN be the Iwasawa decomposition of SO0(1, n) with K = SO(n). Then the “affine Weyl-Poincaré group” Ga = ( R∗+ × AN ) n Rn+1 can be realized as the complex tube domain Π = Rn+1 + iC or the classical Cartan domain BDI(q = 2). The square-integrable representations of G and Ga give the admissible wavelets and wavelet transforms. An ...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

At present, much more soft sensing have been widely used in industrial process control to improve the quality of product and assure safety in production. A novel method using Hilbert-Huang transform (HHT) combined with wavelet support vector machine (WSVM) is put forward. Firstly the method analyzes the intrinsic mode function (IMF) obtained after the empirical mode decomposition (EMD), then ex...

Abstract. The properties of oversampled affine frames are considered here with two main goals in mind. The first goal is to generalize the approach of Chui and Shi to the matrix oversampling setting for expanding, lattice-preserving dilations, whereby we obtain a new proof of the Second Oversampling Theorem for affine frames. The Second Oversampling Theorem, proven originally by Ron and Shen vi...

In this paper, a new method of feature extraction based on design of cubic spline wavelet has been described. Dialectal zone based speaker classification in Marathi language has been attempted in the open set mode using polynomial classifier. The method consists of dividing the speech signal into nonuniform subbands in approximate Mel-scale using an admissible wavelet packet filterbank and mode...

We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the Basis Pursuit and (Orthogonal) Matching Pursuit algorithms to recover a structured representation of an admis...

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be “dilated” by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend ...

We propose a novel method for simultaneous noise reduction and data compression based on shrinking, quantizing and coding the wavelet packet (WP) coeecients. A dynamic programming and fast pruning algorithm is used to eeciently choose the best basis from the entire library of admissible WP bases, and jointly optimize the bit allocation strategy and the quantization scheme in the rate-distortion...

Mel Frequency Cepstral Coefficient (MFCC) features are widely used as acoustic features for speech recognition as well as speaker recognition. In MFCC feature representation, the Mel frequency scale is used to get a high resolution in low frequency region, and a low resolution in high frequency region. This kind of processing is good for obtaining stable phonetic information, but not suitable f...

The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces ...