The behavior of the continuous wavelet and Gabor coefficients in asymptotic limit using stationary phase approximations are investigated. In particular, it is shown how, under some additional assumptions, these allow extraction characteristics analyzed signal, such as frequency amplitude modulation laws. Applications to spectral line estimations matched filtering briefly discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Core Material Construction of Orthonormal Wavelets, R.S. Strichartz An Introduction to the Wavelet Transform on Discrete Sets, M. Frazier and A. Kumar Gabor Frames for L2 Related Spaces, J.J. Benedetto D.F. Walnut Dilation Equations Smoothness Compactly Supported C. Heil D. Colella Remarks Local Fourier Bases, P. Auscher Wavelets Signal Processing The Sampling Theorem, Phi-Transform, Shannon R, Z, T, ZN, R. Torres Frame Decompositions, Sampling, Uncertainty Principle Inequalities, Theory...

The characterization and the separation of amplitude frequency modulated signals is a classical problem signal analysis processing. We present couple new algorithmic procedures for detection ridges in modulus (continuous) wavelet transform one-dimensional (1-D) signals. These are shown to be robust additive white noise. also derive test reconstruction procedure. latter uses only information from restriction sample points ridge. This provides very efficient way code contained signal.

The ridges of the wavelet transform, Gabor or any time-frequency representation a signal contain crucial information on characteristics signal. Indeed, they mark regions plane where concentrates most its energy. We introduce new algorithm to detect and identify these ridges. procedure is based an original form Markov chain Monte Carlo especially adapted present situation. show that this detection useful for noisy signals with multiridge transforms. It common practice among practitioners...

The Linear Time Frequency Analysis Toolbox is a MATLAB/Octave toolbox for computational time-frequency analysis. It intended both as an educational and tool. provides the basic Gabor, Wilson MDCT transform along with routines constructing windows (filter prototypes) manipulating coefficients. also bunch of demo scripts devoted either to demonstrating main functions toolbox, or exemplify their use in specific signal processing applications. In this paper we describe used algorithms,...

We develop an approach for the exploratory analysis of gene expression data, based upon blind source separation techniques. This exploits higher-order statistics to identify a linear model (logarithms of) profiles, described as combinations "independent sources." As result, it yields "elementary patterns" (the "sources"), which may be interpreted potential regulation pathways. Further so-obtained sources show that they are generally characterized by small number specific coexpressed or...

The affine Weyl–Heisenberg group (generated by time and frequency translations, dilations) is considered, some associated resolutions of the identity are derived. As a result, it will be shown that they can all obtained from those with translations analyzed function analyzing reconstructing wavelets.

We describe a new adaptive multiwindow Gabor expansion, which dynamically adapts the windows to signal's features in time-frequency space. The adaptation is based on local sparsity criteria, and also yields as by-product an expansion of signal into layers corresponding different windows. As illustration, we show that simply using two with sizes leads decompositions audio signals transient tonal layers. discuss potential applications detection denoising.

We describe in this paper an audio denoising technique based on sparse linear regression with structured priors. The noisy signal is decomposed as a combination of atoms belonging to two modified discrete cosine transform (MDCT) bases, plus residual part containing the noise. One MDCT basis has long time resolution, and thus high frequency aimed at modeling tonal parts signal, while other short resolution transient (such attacks notes). problem formulated within Bayesian setting. Conditional...

NMR diffusometry and its flagship layout, diffusion-ordered spectroscopy (DOSY), are versatile for studying mixtures of bioorganic synthetic molecules, but a limiting factor applicability is the requirement mathematical treatment capable distinguishing molecules with similar spectra or diffusion constants. We present here processing strategy DOSY, synergy two high-performance blind source separation (BSS) techniques: non-negative matrix factorization (NMF) using additional sparse...

To display the time and frequency content of a given signal large variety techniques exist.In this paper, we give an overview linear time-frequency representations, focusing mainly on two fundamental aspects.The first one is introduction flexibility, more precisely construction waveform systems that can be adapted to specific signals, or processing problems.To do this, base constructions frame theory, which allows lot options, while still ensuring perfect reconstruction.The second aspect...

The articles in this special section on time frequency analysis and applications for its use.

Generalized versions of the entropic (Hirschman- Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version inequality is obtained by introducing generalization coherence. In finite-dimensional case under certain conditions, minimizers these inequalities given. addition, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lp</i> norms introduced as byproducts inequalities.

Current multimedia technologies call for eecient ways of repp resenting signals. We review several methods signal represenn tation, emphasizing potential applications in compression and denoiss ing. pay special attention to the representations which are adapted non-stationaryy features signals, particular classes bilinear resentations, their approximations using time-frequency atoms (mainly wavelet transforms Gabor transforms).