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Concept# Noise reduction

Summary

Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio.
All signal processing devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random with an even frequency distribution (white noise), or frequency-dependent noise introduced by a device's mechanism or signal processing algorithms.
In electronic systems, a major type of noise is hiss created by random electron motion due to thermal agitation. These agitated electrons rapidly add and subtract from the output signal and thus create detectable noise.
In the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In photographic film,

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Environmental noise, mostly related to human activities, has an immense impact on public health. The development of noise reduction technologies is paramount in addressing this problem. Because of practical and economic reasons, a compact, broadband, lightweight, and mechanically robust solution is often compulsory. Existing noise reduction methods typically fall short meeting these requirements. Passive absorbers are bulky and inefficient in the low frequency range or present only a narrowband performance. Active noise reduction methods, including active noise cancellation and acoustic impedance control, appear more promising as they allow extending the bandwidth of operation and remain small compared to a wavelength. An electrodynamic loudspeaker is conventionally a favourable choice for a controlled transducer. However, it limits efficient technology application due to its fragile diaphragm, relatively high weight, and inherent resonant nature, bounding the bandwidth of control.This thesis is devoted to the development of a fundamentally different plasma-based electroacoustic transducer for active sound control applications. The acoustic field is manipulated by the partial ionisation of a thin air layer with an atmospheric corona discharge and its further control with an alternating electrical field. The transducer consists of a set of high voltage wires, separated with a grounded mesh by an air gap. Analytical and numerical models are first developed to design and characterise the corona discharge actuator. Several feedback impedance control strategies are adapted and implemented with the corona discharge actuator, resulting in achieving broadband impedance and sound absorption. A prototype of a plasma-based active acoustic liner for noise reduction under grazing sound incidence is proposed and assessed experimentally in laboratory facilities. A model-based feedforward approach for broadband control of acoustic impedance is then developed. Exploiting the unique physics of the corona discharge actuator with the help of the analytical model, perfect sound absorption and tunable acoustic reflection under normal incidence are achieved over two frequency decades, from several Hz to the kHz range. Such unprecedented bandwidth and compactness of the developed system, along with the simplicity of construction, lightweight, and flexible design, opens new doors in noise control applications, and acoustic metamaterials, among others.

Dorna Bandari, Pascal Frossard

We propose a cross-layer strategy for resource allocation between spatially correlated sources in the uplink of multi-cell FDMA networks. Our objective is to find the optimum power and channel allocation to the different sources, in order to minimize the maximum distortion achieved in decoding any source data in the network. This problem is NP-hard and finding the optimal solution is not computationally feasible. We propose a three-step algorithm to be performed separately in each cell, which finds cross-layer resource allocation in simple steps. This method separates the problem into inter-cell resource management, grouping of sources for joint decoding, and intra-cell channel assignment. For each of these steps we propose methods that satisfy different design constraints and analyze them by simulations. We show that, while using correlation in compression and joint decoding can achieve 25% distortion reduction over independent decoding, the improvement grows to 37% when correlation is also utilized in resource allocation. This significant distortion reduction motivates further work in correlation-aware resource allocation. Overall, our solution is able to achieve a 60% decrease in 5 percentile distortion compared to independent allocation methods.

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.