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In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information. In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling.

Design and development of a haptic feedback demonstrator using time-reversal method and FPGAS

Andrés Chica Linares

The EPFL-LAI is investigating on haptic technologies to give vibrotactile feedback in digital musical interfaces. The aim is to develop an interactive surface that can render a multi-touch vibrotactile stimulus using piezoelectric actuators. The signals that will be sent to the piezoelectric system are generated using deep-learning strategies. Then, they will be simultaneously sent using a FPGA. After this stage there will be a power supply circuit to amplify the digital signals and finally send them to the piezoelectric system. When using these haptic technologies, the sensations of playing a real instrument will be recreated and the player will enjoy the digital instrument through the touch as well. This will make the experience of playing a digital instrument richer.

2021

Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics than the standard Euclidean one. Traditional multiresolution decompositions are restricted to dyadic scales. As first contribution of this thesis, we develop a method that goes beyond this restriction and that is well suited to arbitrary scale-change computations. The key component is a new and numerically exact algorithm for computing inner products between a continuously defined signal and B-splines of any order and of arbitrary sizes. The technique can also be applied for non-uniform to uniform grid conversion, which is another approximation problem where our method excels. Main applications are resampling and signal reconstruction. Although simple to implement, least-squares approximations lead to artifacts that could be reduced if nonlinear methods would be used instead. The second contribution of the thesis is the development of nonlinear spline pyramids that are optimal for lp-norms. First, we introduce a Banach-space formulation of the problem and show that the solution is well defined. Second, we compute the lp-approximation thanks to an iterative optimization algorithm based on digital filtering. We conclude that l1-approximations reduce the artifacts that are inherent to least-squares methods; in particular, edge blurring and ringing. In addition, we observe that the error of l1-approximations is sparser. Finally, we derive an exact formula for the asymptotic Lp-error; this result justifies using the least-squares approximation as initial solution for the iterative optimization algorithm when the degree of the spline is even; otherwise, one has to include an appropriate correction term. The theoretical background of the thesis includes the modelisation of images in a continuous/discrete formalism and takes advantage of the approximation theory of linear shift-invariant operators. We have chosen B-splines as basis functions because of their nice properties. We also propose a new graphical formalism that links B-splines, finite differences, differential operators, and arbitrary scale changes.

EPFL2002

Parallel architecture for high-speed analog-to-digital conversion

Guillaume Ding

Nowadays digital signal processing systems used for radar applications, communication systems or RF measurement equipments, require very high sample-rates. Sometimes these sample-rates are beyond the possibilities offered by conventional ADCs. To overcome these limits parallel architectures have been developed. The most commonly used it the one called "time-interleaved" conversion. This technique allows to achieve very-high sample-rates with circuits working at a lower frequency. The accuracy of "time-interleaved" systems is sensitive to sample-time errors. Some calibration techniques have been developed to reduce this sensitivity. They involve very sophisticated digital signal processing and, in most of the cases, they are not directly implemented on silicon but applied on measurement results in software. The goal of this thesis is to study the feasibility of a new parallel architecture for analog-to-digital conversion. This architecture must present a higher robustness to sample-time errors. The first part of this work is dedicated to time-interleaved converter. An analysis of their sensitivity to several imperfections, such as mismatches and systematic and random sample-time error is presented. This analysis is followed by a description of time-interleaved converter evolution, since the first implemented prototype to the current state of the art of the domain. The second part of this thesis focuses on the development of the new conversion technique called "frequency-interleaved". Two different approaches are studied: the first one is based on a Fourier series decomposition of the signal to convert and the second one is based on a Walsh series decomposition. During this study, theoretical and practical aspects are faced the one with the other, to combine signal processing and microelectronics together. It appears that the Fourier series approach offers modest performances and presents serious problems of implementation. Based on this study, the design of functional blocks of a Walsh series based system is proposed.

EPFL2009