Francesco Gianfelici

Multicomponent AM–FM Representations: An Asymptotically Exact Approach

This paper presents, on the basis of a rigorous mathematical formulation, a multicomponent sinusoidal model that allows an asymptotically exact reconstruction of nonstationary speech signals, regardless of their duration and without any limitation in the modeling of voiced, unvoiced, and transitional segments. The proposed approach is based on the application of the Hilbert transform to obtain an amplitude signal from which an AM component is extracted by filtering, so that the residue can then be iteratively processed in the same way. This technique permits a multicomponent AM-FM model to be derived in which the number of components (iterations) may be arbitrarily chosen. Additionally, the instantaneous frequencies of these components can be calculated with a given accuracy by segmentation of the phase signals. The validity of the proposed approach has been proven by some applications to both synthetic signals and natural speech. Several comparisons show how this approach almost always has a higher performance than that obtained by current best practices, and does not need the complex filter optimizations required by other techniques

Multicomponent AM-FM Demodulation: The State of the Art After the Development of the Iterated Hilbert Transform

This paper presents the state of the art of the multicomponent AM-FM demodulation techniques. On the basis of exhaustive comparisons between the current best practices: the impact of the iterated Hilbert transform on the milestones and the pioneering results of several decades of the advanced research done between MIT, Harvard, Bell-Labs, and NASA, has been analyzed. Finally, past performance, open problems, and future trends of AM-FM models have been considered and discussed.

A novel technique for indirect angular acceleration measurement

This paper presents a novel technique for indirect angular acceleration measurement, based on joint use of four Artificial Neu- ral Networks, which elaborate this processing kind, after opportune transformations of velocity-signal. The result so obtained, is enable to predict the angular acceleration with low delay: making this method- ology suitable in application with high real-time constrains. The de- veloped approach uses Recurrent Neural Networks, which are based on State-Space of Dynamic-Systems, so establishing a direct connec- tion with other approaches based on: Artificial Neural Networks, and Kalman Filters. The indirect measurement of angular acceleration is de- veloped starting from the velocity measure or position sig- nal, generally provided by incremental pulse encoder or dc- tachogenerators (with some postprocessing electronics). The differentiation process amplifies the noise that is unavoid- ably present in measure of velocity or position, thus limiting the application of this indirect measurement. During the last decade some techniques are proposed: they generally predict the acceleration signal by means of Prediction Filters or cas- code compositions of Artificial Neural Networks (1). The ap- proaches, previously described, guarantee an estimation of in- stantaneous acceleration value, which is semi delay-less: this aspect is fundamental in servo motor drive system, where these techniques represent an useful aid to improve the performances of motion control under real-time conditions. Our idea is based on the assumption that there exists a direct connection between the indirect measurement, and the state- space of the system. Along this direction, we think that the velocity-signal represents a specific system. In other words, we assume this signal as a piece-wise linear approximation plus noise: the angular coefficient of every piece-wise linear functions characterizes the system state. Then the problem of indirect angular acceleration measurement can be reformulated as system-state identification with high real-time constrains. This paper presents a novel approach based on joint use of four Artificial Neural Networks (ANNs), which have, as in- puts, four opportune transformations of velocity-signal. Our approach exploits the approximation properties of nonlinear function provided by Artificial Neural Networks, as it is ef- fectively used in (2), where Ovaska et al. use a cascode com- position of Artificial Neural Network, nevertheless with some differences (in our approach): (i) the signals that are ana- lyzed, and processed by the ANNs, are not only the velocity- signal, but signals that are opportunely transformed by contrac- tion operators. (ii) the use of Recurrent Neural Networks (3) that establish direct connections with state-space of Dynamic- System, which determines, and regulates the velocity-signal generation. The obtained result reduces the noise that is unavoidably present on velocity measure, thus it regulates the prediction mechanism based on state characterization of dynamic sys- tem, and finally the representation set (provided by the con- traction operators) permits a better regulation of nondetermin- istic behaviour. The final results have excellent real-time per- formances, and an accuracy that is similar to the actual best practices in this field. The low computational cost of: these operators, and the proposed Artificial Neural Network kind, makes this technique easily implementable On-Chip, and on Embedded System (4).

Efficient Classification of Chaotic Signals with Application to Secure Communications

This paper presents an exhaustive study on the classification capabilities of an efficient algorithm, which is able to accurately classify non-deterministic signals generated by chaotic dynamical systems, without estimating their probability density function (pdf). Experimental results were compared to other existing techniques such as hidden Markov model (HMM), vector quantization (VQ), and dynamic time warping (DTW). Classification performance is higher than current best practices for chaotic signals. A better noise rejection was also achieved, and a reduction of two orders of magnitude in training-times compared with HMM was obtained, thus making the proposed methodology one of the current best practices in this field. As an application example, the recognition of encrypted chaotic-signals in a secure-communication context, is reported and discussed.

Information theoretical algorithm based on statistical models for blind identification of nonstationary dynamical systems

This paper presents an effective blind statistical identification technique for nonstationary nonlinear systems based on an information theoretical algorithm. This technique firstly extracts, from the output signals, the multivariate relationships in the Hilbert spaces by exploiting the separability properties of the signal outputs transformed by the Karhunen-Loève transform (KLT). Then, the algorithm methodologically clusters the stochastic surfaces in the Hilbert spaces using the self-organizing maps (SOMs) and further develops their best statistical model under the fixed-rank condition. The resulting blind identification of the statistical system model is based on marginal probability density functions (PDFs), whose convergence to the statistical system model based on Monte Carlo simulations has also been demonstrated by asymptotically vanishing the Kullback-Leibler divergences. A large number of simulations on both synthetic and real systems demonstrated the validity and the excellent performances of this technique that is irrespective of the system order, the stochastic surface topology, the true marginal PDFs, and the knowledge of the statistics of the noise superimposed to the output signals. Finally, this approach could also represent a suitable and promising technique for the noninvasive diagnosis of a large class of medical pathologies originated by unknown physiological factors (nonlinear compositions of unknown input signals) and/or when they are difficult or unpractical to measure.

Sensor Network-Based Nonlinear System Identification

In this paper, a new algorithm for the identification of distributed systems by large scale collaborative sensor networks is suggested. The algorithm, that uses the distributed Karhunen-Loeve transform, extends in a decentralized setting the KLT-based identification approach that have recently been proposed for a centralized setting. The effectiveness of the proposed methodology is directly related to the reduction of total distortion in the compression performed by the single nodes of the sensor network, to the identification accuracy as well as to the low computational complexity of the fusion algorithm performed by the fusion center to regulate the intelligent cooperation of the nodes. The results in the identification of a system whose behavior is described by a partial differential equation in a 2-D domain with random excitation confirms the effectiveness of this technique.

A Non Probabilistic Algorithm Based on Karhunen-Loève Transform for the Recognition of Stochastic Signals

This paper proposes an efficient methodology that is able to accurately recognize nondeterministic signals generated by stochastic processes (SPs). This technique is based on (i) a training algorithm, which iteratively extracts suitable parameter collections; (ii) a recognition procedure that measures the trajectory-proximities by means of an ad-hoc metric, in order to associate the unknown signal to an SP by using a representation based on Karhunen-Loeve transform (KLT). The recognition algorithm exploits a modelling of several signal classes based on KLT, inasmuch this representation effectively characterizes projections of every SP signal in terms of nondeterministic trajectories defined on associated spaces. The methodology is able to recognize SPs without probability density function (pdf) estimation, and with low-computational complexity: exhaustive experimentations on specific case-studies have shown high recognition performance. As application examples, SPs generated by stochastic nonlinear-differential-equations (SNDEs), with different initial conditions and coefficients being random variables (RVs), have been considered

A novel touch screen technology based on: stochastic process theory and fuzzy logic approach

The growing interest for touch screen technologies is prin- cipally motivated by: the increasing use in electronic devices, and the demand of high interactivity in human-machine interfaces. The Analogical Resistive Touch Screens (ARTS) represent the actual best practices in this field: this aspect is principally imputable to their capabilities of nondeterminism regulation, and their accuracy. Nev- ertheless the increasing request of preciseness in the touched point identification, actually represents an open problem. In this paper a novel technique, based on joint use of stochastic process theory, and fuzzy-logic approach, is proposed. The effectiveness of this methodol- ogy is principally imputable to the coordination of information, data, and control parameters that derive by different levels of abstraction.

Computational Intelligence for the Collaborative Identification of Distributed Systems

In this chapter, on the basis of a rigorous mathematical formulation, a new algorithm for the identification of distributed systems by large scale collaborative sensor networks is suggested. The algorithm extends a KLT-based identification approach to a decentralized setting, using the distributed Karhunen-Loeve transform (DKLT) recently proposed by Gastpar et al.. The proposed approach permits an arbitrarily accurate identification since it exploits both the asymptotic properties of convergence of DKLT and the universal approximation capabilities of radial basis functions neural networks. The effectiveness of the proposed approach is directly related to the reduction of total distortion in the compression performed by the single nodes of the sensor network, to the identification accuracy, as well as to the low computational complexity of the fusion algorithm performed by the fusion center to regulate the intelligent cooperation of the nodes. Some identification experiments, that have been carried out on systems whose behavior is described by partial differential equations in 2-D domains with random excitations, confirm the validity of this approach. It is worth noting the generality of the algorithm that can be applied in a wide range of applications without limitations on the type of physical phenomena, boundary conditions, sensor network used, and number of its nodes.

Methods of Information Geometry (Amari, S. and Nagaoka, H.; 2000) [Book review]

This book presents the state of the art, the current best practices and the innovative techniques of the methods of information geometry. The first half of the book presents a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections. The second half describes many applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. This is a well-written book, original and highly relevant from which to learn methods and results.