Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique which is robust against multipath fading and very easy to implement in transmitters and receivers using the inverse fast Fourier transform and the fast Fourier transform. A guard interval using cyclic prefix is inserted in each OFDM symbol to avoid the inter-symbol interference. This guard interval should be at least equal to, or longer than the maximum delay spread of the channel to combat against inter-symbol interference properly.<p> In coherent detection, channel estimation is required for the data detection of OFDM systems to equalize the channel effects. One of the popular techniques is to insert pilot tones (reference signals) in OFDM symbols. In conventional method, pilot tones are inserted into every OFDM symbols. Channel capacity is wasted due to the transmission of a large number of pilot tones. To overcome this transmission loss, incoherent data detection is introduced in OFDM systems, where it is not needed to estimate the channel at first. We use differential modulation based incoherent detection in this thesis for the data detection of OFDM systems. Data can be encoded in the relative phase of consecutive OFDM symbols (inter-frame modulation) or in the relative phase of an OFDM symbol in adjacent subcarriers (in-frame modulation). We use higher order differential modulation for in-frame modulation to compare the improvement of bit error rate. It should be noted that the single differential modulation scheme uses only one pilot tone, whereas the double differential uses two pilot tones and so on. Thus overhead due to the extra pilot tones in conventional methods are minimized and the detection delay is reduced. It has been observed that the single differential scheme works better in low SNRs (Signal to Noise Ratios) with low channel taps and the double differential works better at higher SNRs. Simulation results show that higher order differential modulation schemes don¡¯t have any further advantages. For inter-frame modulation, we use single differential modulation where only one OFDM symbol is used as a reference symbol. Except the reference symbol, no other overhead is required. We also perform channel estimation using differential modulation. Channel estimation using differential modulation is very easy and channel coefficients can be estimated very accurately without increasing any computational complexity. Our simulation results show that the mean square channel estimation error is about ¡¼10¡½^(-2) at an SNR of 30 dB for double differential in-frame modulation scheme, whereas channel estimation error is about ¡¼10¡½^(-4) for single differential inter-frame modulation. Incoherent data detection using classical DPSK (Differential Phase Shift Keying) causes an SNR loss of approximately 3 dB compared to coherent detection. But in our method, differential detection can estimate the channel coefficients very accurately and our estimated channel can be used in simple coherent detection to improve the system performance and minimize the SNR loss that happens in conventional method.

This dissertation proposes new methods for measuring jitter of high-speed digital signals. The proposed techniques are twofold. First, a low-speed jitter measurement environment is realized by using a jitter expansion sensor. This sensor uses a low-frequency reference signal as compared to high-frequency reference signals required in standard high-speed signal jitter measurement instruments. The jitter expansion sensor generates a low-speed signal at the output, which contains jitter content of the original high-speed digital signal. The low-speed sensor output signal can be easily acquired with a low-speed digitizer and then analyzed for jitter. The proposed low-speed jitter measurement environment using the jitter expansion sensor enhances the reliability of current jitter measurement approaches since low-speed signals used as a reference signal and a sensor output signal can be generated and applied to measurement systems with reduced additive noise. The second approach is direct digitization without using a sensor, in which a high-speed digital signal with jitter is incoherently sub-sampled and then reconstructed in the discrete-time domain by using digital signal reconstruction algorithms. The core idea of this technique is to remove the hardware required in standard sampling-based jitter measurement instruments for time/phase synchronization by adopting incoherent sub-sampling as compared to coherent sub-sampling and to reduce the need for a high-speed digitizer by sub-sampling a periodic signal over its many realizations. In the proposed digitization technique, the signal reconstruction algorithms are used as a substitute for time/phase synchronization hardware. When the reconstructed signal is analyzed for jitter in digital post-processing, a self-reference signal is extracted from the reconstructed signal by using wavelet denoising methods. This digitally generated self-reference signal alleviates the need for external analog reference signals. The self-reference signal is used as a timing reference when timing dislocations of the reconstructed signal are measured in the discrete-time domain. Various types of jitter of the original high-speed reference signals can be estimated using the proposed jitter analysis algorithms.

An \emph {explicit} algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in {3-D}. By using ideas from ``\emph{compressed sensing}'', we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume{,} thereby reducing the size of the operators. According {to} compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is \emph{incoherent} with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operatoion. A proof of principle for the ``compressed sensing'' method is given for wavefield extrapolation in {2-D}. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator.

This thesis describes an experimental investigation of high frequency acoustic wave scattering from turbulent premixed flames. The objective of this work was to characterize the scattered incoherent acoustic field and determine its parametric dependence on frequency, flame brush thickness, incident and measurement angles, mean velocity and flame speed. The experimental facility consists of a slot burner with a flat flame sheet that is approximately 15 cm wide and 12 cm tall. The baseline cold flow characteristics and flame sheet statistics were extensively characterized. Studies were performed over a wide range of frequencies (1-24 kHz) in order to characterize the role of the incident acoustic wave length. The spectrum of the scattered acoustic field showed distinct incoherent spectral sidebands on either side of the driving frequency. The scattered incoherent field was characterized in terms of the incoherent field strength and spectral bandwidth and related to the theoretical predictions. The role of the flame front wrinkling scale, i.e., flame brush thickness, was also studied. Flame brush thickness was varied independent of the mean velocity and flame speed by using a variable turbulence generator. Results are reported for five flame brush thickness cases, ranging from 1.2 mm to 5.2 mm. Some dependence of scattered field characteristics on flame brush thickness was observed, but the magnitude of the effect was much smaller than expected from theoretical considerations. The spatial dependence of the scattered field was investigated by measuring the scattered field at four measurement angles and exciting the flame at four incident angles. Theory predicts that these variations influence the spatial scale of the acoustic wave normal to the flame, a result confirmed by the measurements. Measurements were performed for multiple combinations of mean velocities and flame speeds. The scattered field was observed to depend strongly on the flame speed. Further analysis suggested that the change in orientation angle distribution with flame speed had a large influence on the scattered field. The scattered field characteristics did not show any appreciable change with mean velocity. This result was expected since flame brush thickness characteristics themselves exhibit a weak velocity dependence.

My research on the new concepts for spectrometer has been focused on the development of true multi-dimensional spectrometers, which use a multi-dimensional [two-dimensional (2D) or 3D] mapping of the spectral information into space. I showed that by combining a simple dispersive element (a volume hologram) formed in very inexpensive polymers with a basic Fabry-Perot interferometer, we can form a spectrometer with ultra-high resolution over a large spectral bandwidth, which surpasses all conventional spectrometers. I strongly believe that the extension of this mapping into three dimensions by using synthetic nanophotonic structures with engineered dispersion can further improve the performance and reduce the overall spectrometer size into the micron regime. The need for efficient modeling and simulation tools comes from the sophisticated nature of the new 3D nanophotonic structures, which makes their simple analysis using well-known simple formulas for the propagation of the electromagnetic fields in bulk materials impossible. In my Ph.D. research, I developed new approximate modeling tools for both the modeling of incoherent sources in nanophotonics, and for the propagation of such optical beams inside the 3D nanophotonic structures of interest with several orders of magnitude improvement in the simulation speed for practical size devices without sacrificing accuracy. To enable new dispersive properties using a single nanophotonic structure, I have focused in my Ph.D. research into polymer-based 3D photonic crystals, which can be engineered using their geometrical features to demonstrate unique dispersive properties in three dimensions that cannot be matched by any bulk material even with orders of magnitude larger sizes. I have demonstrated the possibilities of using a very compact structure for wavelength demultiplexing and also for spectroscopy without adding any other device.

This thesis explores the theory describing wavefunctions and images, both elastic and inelastic, formed in scanning transmission electron microscopy. / A method is presented for calculating the elastic wavefunction based upon a new formulation of the boundary conditions which couples the probe to Bloch states within the crystal in a single step. Though this method is fundamentally equivalent to previous approaches based upon the superposition of wavefunctions corresponding to individual plane wave components in the incident probe, it provides new insight into the some of the dynamics, allows for efficient calculations, and proves useful for demonstrating well known results such as reciprocity relations. A formal inversion technique is also presented that uses a collection of diffraction plane data in scanning transmission electron microscopy to reconstruct the object potential, even in the presence of strong multiple scattering. / The new form of the boundary conditions allows for a generalization of a crosssection expression for calculating inelastic images, making use of the theory of mixed dynamic form factors. This enables the simulation of images for a range of inelastic mechanisms, including thermal scattering, used to simulate high-angle annular dark field imaging, and inner-shell ionization, used to simulate electron energy loss spectroscopy images. A multislice form of this expression is given. Selection between the methods can thus be based on the sample of interest: the Bloch wave method is very efficient when the sample is crystalline; the multislice method is more appropriate if the sample lacks periodicity. / The issue of cross-talk, where dynamical probe spreading may result in a signal containing contributions from several columns and therefore confound direct interpretation, is assessed for high-angle annular dark field imaging. Single atom images are simulated to provide an estimate of the localization of signal in electron energy loss spectroscopy, and confirm that the limitations of probe size generally outweigh those of the nature of the ionization interaction. The feasibility of column-by-column spectroscopic identification is demonstrated through a combination of experimental data and supporting calculations. Data demonstrating the location and spectroscopic identification of a single impurity atom in the bulk are supported by simulation and it is demonstrated that a quantitative comparison can offer further useful information: an estimate for the depth of the impurity. / The contribution to electron energy loss spectroscopy images from electrons which have undergone thermal scattering prior to causing an inner-shell ionization event is assessed. It is concluded that this contribution is significant in strongly scattering specimens imaged using fine probes. It will be necessary to include this contribution if quantitative comparisons are to be made.

Incoherent scatter radar (ISR) measurements were used in conjunction with plasma simulations to study two micro-scale plasma processes that commonly occur in the auroral ionosphere. These are 1) ion acoustic turbulence and 2) Langmuir turbulence. Through an ISR experiment we investigated the dependence of ion acoustic turbulence on magnetic aspect angle. The results showed a very strong aspect angle sensitivity which could be utilized to classify the turbulence according to allowable generation mechanisms and sources of free energy. In addition, this work presents results that led to the discovery of a new type of ISR echo, explained as a signature of cavitating Langmuir turbulence. A number of incoherent scatter radar experiments, exploiting a variety of beam and pulse patterns, were designed or revisited to investigate the Langmuir turbulence underlying the radar echoes. The experimental results revealed that Langmuir turbulence is a common feature of the auroral ionosphere. The experimental efforts also led to uncovering a relationship between Langmuir turbulence and one type of natural electromagnetic emission that is sometimes detected on the ground, so-called “medium frequency burst”, providing an explanation for the generation mechanism of these emissions. In an attempt to gain insights into the source mechanism underlying Langmuir turbulence, 1-dimensional Zakharov simulations were employed to study the interactions of ionospheric electron beams with a broad range of parameters with the background plasma at the F region peak. A variety of processes were observed, ranging from a cascade of parametric decays, to formation of stationary wave packets and density cavities in the condensate region, and to direct nucleation and collapse at the initial stage of the turbulence. The simulation results were then compared with the ISR measurements where inconsistencies were found in the spectral details and intensity of the simulated and measured Langmuir turbulence echoes, suggesting the possibility that the direct energy for the turbulence was provided by unstable low-energy (5 − 20 eV) electron populations produced locally in the F region of the ionosphere rather than by electron beams originating from the magnetosphere.

This diploma thesis discusses methods of dictionary learning to inpaint missing sections in the audio signal. There was theoretically analyzed and practically used algorithms K-SVD and INK-SVD for dictionary learning. These dictionaries have been applied to the reconstruction of audio signals using OMP (Orthogonal Matching Pursuit). Furthermore, there was proposed an algorithm for selecting the stationary segments and their subsequent use as training data for K-SVD and INK-SVD. In the practical part of thesis have been observed efficiency with training set selection from whole signal compared with algorithm for stationary segmentation used. The influence of mutual coherence on the quality of reconstruction with incoherent dictionary was also studied. With created scripts for multiple testing in Matlab, there was performed comparison of these methods on genre distinct songs.

<div>The widely accepted Non-equilibrium Greens functions (NEGF) method and the Self-Consistent Born Approximation, to include scattering, is employed. Due to the large matrix sizes typically needed when solving Greens functions, an efficient recursive algorithm is typically utilized. However, the current state of the art of this so-called recursive Greens function algorithm only allows the inclusion of local scattering or non-locality within a limited range. Most scattering mechanisms are Coulombic and are therefore non-local. Recently, we have developed an addition to the recursive Greens function algorithm that can handle arbitrary non-locality. Validation and performance will be assessed for nanowires.</div><div><br></div><div>The second half of this work discusses the modeling of an active ingredient in a liquid environment. The state of the art is outlined with options for different modeling approaches - mainly the implicit and the explicit solvation model. Extensions of the explicit model to include an open, quantum environment is the main work of the second half. First results for an extension of the commonly used molecular dynamics with thermodynamic integration are also presented.</div>

Diffusion multiple et non linéarité sont deux phénomènes antagonistes en acoustique, ilest ainsi rare d’observer un couplage de ces deux effets. En acoustique, les effets non linéaires sontimportants souvent lorsqu’ils sont cumulatifs, or la diffusion multiple modifie la relation de dispersiondu milieu et empêche ainsi ce caractère cumulatif. Les bulles sont connues pour avoir un comportementnon linéaire. Elles sont aussi de très bons diffuseurs avec une section efficace de diffusion qui est trèsgrande devant leur section efficace géométrique notamment à leur fréquence de résonance. Les milieuxbulleux semblent ainsi de bons candidats pour observer de la diffusion multiple en régime non linéaire.Trois régimes sont observables dans un milieu bulleux : un régime basse fréquence auquel les effetsnon linéaires sont importants et cumulatifs mais sans diffusion multiple, un régime à la fréquence derésonance des bulles auquel les effets non linéaires ne sont pas cumulatifs mais restent quand mêmeélevés tout comme la diffusion bien qu’atténuée par l’absorption du milieu, et enfin un régime hautefréquence pour lequel les effets de diffusion multiple sont importants mais les effets non linéaires sontabsents. Les travaux décrits dans cette thèse ont porté sur la modélisation et l’expérimentation desrégimes à la fréquence de résonance et à haute fréquence. A haute fréquence, l’observation d’une codadans les milieux bulleux est modélisée par une équation de diffusion. A la fréquence de résonance, lamodélisation, validée par les expériences, conduit ensuite à des applications qui sont : le doubleur defréquence, la diode acoustique et le miroir à conjugaison de phase. / Multiple scattering and non linear effects are antagonists so it is not commun to observea coupling of those two effects. In acoustics, non linear effects are important when they are cumulative,therefore dispersion relation is modified by multiple scattering and non linear effects cannotbe cumulative. Bubbles are known to have a non linear behavior and also to be good scatterers witha scattering cross section higher than the geometric cross section at resonance frequency. Therefore,bubbly media seem to be good to observe multiple scattering in non linear regime. A bubbly-mediumhas three different regimes. At low frequency, non linear effects are important and cumulative butthere is no multiple scattering effects. At bubbles resonance frequency, non linear behavior and alsomultiple scattering effects are important but the non linear effects cannot be cumulative. At high frequency,multiple scattering effects are important but without no non linear effects. The experimentsin this thesis show, on the one hand, a high frequency wave propagating in a bubbly-medium andon the other hand, the resonance frequency wave propagation. At high frequency, a coda is observedin experiment and modeled by a diffusion equation. At resonance frequency, the model, confirmed bythe experiments, leads us to some applications : acoustic frequency doubler, acoustic diode and phaseconjugation mirror.