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Concept

Noise

Summary

Noise is unwanted sound considered unpleasant, loud, or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound. Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, noise in electronics may not be audible to the human ear and may require instruments for detection. In audio engineering, noise can refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as a hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting. In experimental sciences, noise can refer to any random fluctuations of data that hinders perception of a signal. Measurement Sound is measured based on the amplitude and frequency of a sound wave. Amplitude measures how forceful the wave is. The

Official source

https://en.wikipedia.org/wiki/Noise

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Adaptive noise cancelling systems for acoustic wearable device

Mohamed Ben Arbia

Acoustic noise is present in many environments. Such noise is undesirable and provides a poor listening experience. Active noise cancellation refers to the fact of reducing undesired noise using a cancelling signal emitted trough a secondary source. Many methods are proposed to perform active noise cancellation on headphones. In this work, we are interested in performing digital active noise cancellation for a wearable device. There are many challenges for such a system. The noise cancellation process has to be performed in real time therefore as fast as possible. Besides, all the operations of such a system has to be digitally processed. Therefore, one of the most important points is to evaluate the performance of the different methods and algorithms needed for performing digital active noise cancellation on real time.

2015

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another. Both vanishing Dirichlet and Neumann boundary conditions are considered.We first study the nonlinear SHE in any space dimension with multiplicative correlated noise and bounded initial data. We prove that the solutions to SHE on an increasing sequence of domains converge exponentially fast to the solution to SHE on

\R^d.

Uniform convergence on compact set is obtained for all

p

-moments. The conditions that need to be imposed on the noise are the same as those required to ensure existence of a random field solution. A Gronwall-type iteration argument is used together with uniform bounds on the solutions, which are surprisingly valid for the entire sequence of increasing domains.We then study SHE in space dimension

d\ge 2

with additive white noise and bounded initial data. Even though both solutions need to be considered as distributions, their difference is proved to be smooth. If fact, the order of smoothness depends only on the regularity of the boundary of the increasing sequence of domains. We prove that the Fourier transform, in the sense of distributions, of the solution to SHE on

\R^d

do not have any locally mean-square integrable representative. Therefore, convergence is studied in local versions of Sobolev spaces. Again, exponential rate is obtained.Finally, we study the Anderson model for SHE with correlated noise and initial data given by a measure. We obtain a special expression for the second moment of the difference of the solution on

\R^d

with that on a bounded domain. The contribution of the initial condition is made explicit. For example, exponentially fast convergence on compact sets is obtained for any initial condition with polynomial growth. More interestingly, from a given convergence rate, we can decide whether some initial data is admissible.

EPFL2022

A novel frequency synthesizer with a strong emphasis on low-power consumption (2mW) was developed for this thesis. A BAW-resonator was used for the design of the high-frequency oscillator. The BAW's high Q-Factor ensured a minimal power consumption, while providing outstanding phase noise performance. This type of frequency synthesizer can be implemented in practically every mobile wireless system standard, which is relying on batteries as the power supply, such as Bluetooth, Zigbee and others. For this work, a Bluetooth-compatible standard was taken in order to derive the system specifications. The frequency synthesizer then was designed and implemented in a 180nm CMOS process. The approach of the "Sliding-IF" architecture was chosen and modified in order to take full advantage on the BAW oscillator. Therefore a two-stage frequency translation of the signal was necessary, similar to the super-heterodyne transceiver topology. The channel selection and the frequency error correction is done at the second stage, since the BAW-based oscillator does practically not provide any frequency tuning. For this, a Delta-Sigma-Modulator based Fractional-N PLL was developed. A system supply voltage of 1.2V was chosen in order to keep power consumption as low as possible. This supply voltage can also be easily supplied by AA or AAA-batteries and a low-voltage regulator. The most important technique to reduce overall power consumption was to reduce the high-frequency requirements to the system blocks. This was done by modifying the "Sliding-IF" architecture and by the use of the BAW resonator. The minimization of the power consumption required careful choice and design of each of the system blocks. For this, several approaches were analyzed, especially the topology of each block and its optimization were important. A special emphasis on the analysis, design and discussion was also made on the noise, and especially the phase noise. A ring oscillator, a LC-VCO and a BAW-oscillator were implemented and measured in order to validate the theory and the simulation results. The complete frequency synthesizer with an Automatic Amplitude Control, Frequency Dividers, Mixer, Charge-Pump, Phase-Frequency Detector and a Delta-Sigma-Modulator was designed and implemented. This thesis was elaborated in the frame of the MiNAMI and MiMOSA projects of the European research programme (FP6).

EPFL2009

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

\R^d.

Uniform convergence on compact set is obtained for all

p

d\ge 2

\R^d

\R^d

EPFL2022