Wavelet packet decompositions based on tree structured 2-channel filter banks with conjugate quadrature filters (CQF) have recently found many applications in the area of audio coding. Their time-frequency tiling is dual to that of timevarying modulated lapped transforms (MLT). In this paper we present a new orthonormal wavelet packet basis, which is constructed by frequency-varying MLT. These ...

The aim of this article is to study the attenuation transient low-frequency waves in 2D lattices both plane and antiplane problems. main idea that analytical solutions problems mechanics discrete periodic media can be obtained by a method asymptotic inversion Laplace Fourier transforms vicinity quasi-front infinitely long waves; moreover, it possible take into account contribution short waves. ...

Both from a mathematical as well as a biological perspective, Wavelet transforms present themselves as an attractive means for extracting low-level information from an image. We present a processor-time optimal algorithm to implement wavelet transforms on a VLSI implementable parallel digital architecture. A desirable initial processing step in an artiicial vision system is the identiication of...

In the paper, we present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction, we used the interpolatory discrete splines, which enabled us to design a library of perfect reconstruction filterbanks. These filterbanks are related to Butterworth filters. The construction is performed in a “lifting” manner. The dif...

The purpose of this paper is to compare competing techniques for wideband channelisation, and to assess the flexibility of each of these methods in the context of a software defined radio (SDR) receiver. Distinction is drawn between architectures where all channels are equally spaced and of equal bandwidth, and those architectures which afford greater flexibility. The architecture requires that...

We present new multiwavelet transforms of multiplicity 2 for manipulation of discrete-time signals. The transforms are implemented in two phases: 1) Pre (post)-processing, which transforms the scalar signal into a vector signal (and back) and 2) wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting ...

A family of Gaussian analytic functions (GAFs) has recently been linked to the Gabor transform white noises [4]. This answered pioneering work by Flandrin [10], who observed that zeros noise had a regular distribution and proposed filtering algorithms based on spectrogram. In this paper, we study in systematic way link between GAFs class time-frequency transforms noises. Our main observation is...

We review traditions and trends in optics and imaging recently arising by applying programmable optical devices or by sophisticated approaches for data evaluation and image reconstruction. Furthermore, a short overview is given about modeling of well-known classical optical elements, and vice versa, about optical realizations of classical mathematical transforms, as in particular Fourier, Hilbe...