Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the $M$-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency.Comment: Submitted to the IEEE Transactions on Signal Processing, October 200

Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation

International audienceThis work provides asymptotic properties of the autocorrelation functions of the wavelet packet coefficients of a fractional Brownian motion. It also discusses the convergence speed to the limit autocorrelation function, when the input random process is either a fractional Brownian motion or a wide-sense stationary second-order random process. The analysis concerns some families of wavelet paraunitary filters that converge almost everywhere to the Shannon paraunitary filters. From this analysis, we derive wavelet packet based spectrum estimation for fractional Brownian motions and wide-sense stationary random processes. Experimental tests show good results for estimating the spectrum of 1/f processes

Identifying informative signs for the recognition of non-stationary signals of information-measuring systems on the base of spectral analysis and filtration on the wavelet basis

To identify the informative signs used in the procedure of recognition of non-stationary signals of information-measuring systems are suggested to use spectral analysis based on discrete wavelet-transformation and filtrationin the wavelet display area. Informative signs are formed via processing of useful signalsobtained by filtrationand recognition signalsare produced on the base of these signs

Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases

International audienceThe paper addresses image feature characterization and the structuring of large and heterogeneous image databases through the stochasticity or randomness appearance. Measuring stochasticity involves finding suitable representations that can significantly reduce statistical dependencies of any order. Wavelet packet representations provide such a framework for a large class of stochastic processes through an appropriate dictionary of parametric models. From this dictionary and the Kolmogorov stochasticity index, the paper proposes semantic stochasticity templates upon wavelet packet sub-bands in order to provide high level classification and content-based image retrieval. The approach is shown to be relevant for texture images

Investigating self-similarity and heavy-tailed distributions on a large scale experimental facility

International audienceAfter the seminal work by Taqqu et al. relating selfsimilarity to heavy-tailed distributions, a number of research articles verified that aggregated Internet traffic time series show self-similarity and that Internet attributes, like Web file sizes and flow lengths, were heavy-tailed. However, the validation of the theoretical prediction relating self-similarity and heavy tails remains unsatisfactorily addressed, being investigated either using numerical or network simulations, or from uncontrolled Web traffic data. Notably, this prediction has never been conclusively verified on real networks using controlled and stationary scenarii, prescribing specific heavy-tailed distributions, and estimating confidence intervals. With this goal in mind, we use the potential and facilities offered by the large-scale, deeply reconfigurable and fully controllable experimental Grid5000 instrument, to investigate the prediction observability on real networks. To this end we organize a large number of controlled traffic circulation sessions on a nation-wide real network involving two hundred independent hosts. We use a FPGA-based measurement system, to collect the corresponding traffic at packet level. We then estimate both the self-similarity exponent of the aggregated time series and the heavy-tail index of flow size distributions, independently. On the one hand, our results complement and validate with a striking accuracy some conclusions drawn from a series of pioneer studies. On the other hand, they bring in new insights on the controversial role of certain components of real networks

Investigating self-similarity and heavy tailed distributions on a large scale experimental facility

After seminal work by Taqqu et al. relating self-similarity to heavy tail distributions, a number of research articles verified that aggregated Internet traffic time series show self-similarity and that Internet attributes, like WEB file sizes and flow lengths, were heavy tailed. However, the validation of the theoretical prediction relating self-similarity and heavy tails remains unsatisfactorily addressed, being investigated either using numerical or network simulations, or from uncontrolled web traffic data. Notably, this prediction has never been conclusively verified on real networks using controlled and stationary scenarii, prescribing specific heavy-tail distributions, and estimating confidence intervals. In the present work, we use the potential and facilities offered by the large-scale, deeply reconfigurable and fully controllable experimental Grid5000 instrument, to investigate the prediction observability on real networks. To this end we organize a large number of controlled traffic circulation sessions on a nation-wide real network involving two hundred independent hosts. We use a FPGA-based measurement system, to collect the corresponding traffic at packet level. We then estimate both the self-similarity exponent of the aggregated time series and the heavy-tail index of flow size distributions, independently. Comparison of these two estimated parameters, enables us to discuss the practical applicability conditions of the theoretical prediction

The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena

The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex System

Search for gravitational wave bursts by wavelet packet decomposition: The detection algorithm

We present a novel method based on wavelet packet transformation for detection of gravitational wave (gw) bursts embedded in additive Gaussian noise. The method exploits a wavelet packet decomposition of observed data and performs detection of bursts at multiple time-frequency resolutions by the extreme value statistics. We discuss the performances of detection algorithms (efficiency and robustness) in the general framework of hypothesis testing. In particular, we compare the performances of wavelet packet (WP), matched filter (MF), and power filter (PF) algorithms by means of a complete Monte Carlo simulation of the output of a gw detector, with the detection efficiencies of MF and PF playing the role of upper and lower bounds, respectively. Moreover, the performances of impulsive filter (IF) algorithm, widely used in the data analysis of resonant gw detectors, have been investigated. Results we get by injecting chirplet signals confirm the expected performances in terms of efficiency and robustness. To illustrate the application of the new method to real data, we analyzed a few data sets of the resonant gw detector AURIGA

An investigation into the requirements for an efficient image transmission system over an ATM network

This thesis looks into the problems arising in an image transmission system when transmitting over an A TM network. Two main areas were investigated: (i) an alternative coding technique to reduce the bit rate required; and (ii) concealment of errors due to cell loss, with emphasis on processing in the transform domain of DCT-based images. [Continues.