Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement

Seismic characterisation based on time-frequency spectral analysis

We present high-resolution time-frequency spectral analysis schemes to better resolve seismic images for the purpose of seismic and petroleum reservoir characterisation. Seismic characterisation is based on the physical properties of the Earth's subsurface media, and these properties are represented implicitly by seismic attributes. Because seismic traces originally presented in the time domain are non-stationary signals, for which the properties vary with time, we characterise those signals by obtaining seismic attributes which are also varying with time. Among the widely used attributes are spectral attributes calculated through time-frequency decomposition. Time-frequency spectral decomposition methods are employed to capture variations of a signal within the time-frequency domain. These decomposition methods generate a frequency vector at each time sample, referred to as the spectral component. The computed spectral component enables us to explore the additional frequency dimension which exists jointly with the original time dimension enabling localisation and characterisation of patterns within the seismic section. Conventional time-frequency decomposition methods include the continuous wavelet transform and the Wigner-Ville distribution. These methods suffer from challenges that hinder accurate interpretation when used for seismic interpretation. Continuous wavelet transform aims to decompose signals on a basis of elementary signals which have to be localised in time and frequency, but this method suffers from resolution and localisation limitations in the time-frequency spectrum. In addition to smearing, it often emerges from ill-localisation. The Wigner-Ville distribution distributes the energy of the signal over the two variables time and frequency and results in highly localised signal components. Yet, the method suffers from spurious cross-term interference due to its quadratic nature. This interference is misleading when the spectrum is used for interpretation purposes. For the specific application on seismic data the interference obscures geological features and distorts geophysical details. This thesis focuses on developing high fidelity and high-resolution time-frequency spectral decomposition methods as an extension to the existing conventional methods. These methods are then adopted as means to resolve seismic images for petroleum reservoirs. These methods are validated in terms of physics, robustness, and accurate energy localisation, using an extensive set of synthetic and real data sets including both carbonate and clastic reservoir settings. The novel contributions achieved in this thesis include developing time-frequency analysis algorithms for seismic data, allowing improved interpretation and accurate characterisation of petroleum reservoirs. The first algorithm established in this thesis is the Wigner-Ville distribution (WVD) with an additional masking filter. The standard WVD spectrum has high resolution but suffers the cross-term interference caused by multiple components in the signal. To suppress the cross-term interference, I designed a masking filter based on the spectrum of the smoothed-pseudo WVD (SP-WVD). The original SP-WVD incorporates smoothing filters in both time and frequency directions to suppress the cross-term interference, which reduces the resolution of the time-frequency spectrum. In order to overcome this side-effect, I used the SP-WVD spectrum as a reference to design a masking filter, and apply it to the standard WVD spectrum. Therefore, the mask-filtered WVD (MF-WVD) can preserve the high-resolution feature of the standard WVD while suppressing the cross-term interference as effectively as the SP-WVD. The second developed algorithm in this thesis is the synchrosqueezing wavelet transform (SWT) equipped with a directional filter. A transformation algorithm such as the continuous wavelet transform (CWT) might cause smearing in the time-frequency spectrum, i.e. the lack of localisation. The SWT attempts to improve the localisation of the time-frequency spectrum generated by the CWT. The real part of the complex SWT spectrum, after directional filtering, is capable to resolve the stratigraphic boundaries of thin layers within target reservoirs. In terms of seismic characterisation, I tested the high-resolution spectral results on a complex clastic reservoir interbedded with coal seams from the Ordos basin, northern China. I used the spectral results generated using the MF-WVD method to facilitate the interpretation of the sand distribution within the dataset. In another implementation I used the SWT spectral data results and the original seismic data together as the input to a deep convolutional neural network (dCNN), to track the horizons within a 3D volume. Using these application-based procedures, I have effectively extracted the spatial variation and the thickness of thinly layered sandstone in a coal-bearing reservoir. I also test the algorithm on a carbonate reservoir from the Tarim basin, western China. I used the spectrum generated by the synchrosqueezing wavelet transform equipped with directional filtering to characterise faults, karsts, and direct hydrocarbon indicators within the reservoir. Finally, I investigated pore-pressure prediction in carbonate layers. Pore-pressure variation generates subtle changes in the P-wave velocity of carbonate rocks. This suggests that existing empirical relations capable of predicting pore-pressure in clastic rocks are unsuitable for the prediction in carbonate rocks. I implemented the prediction based on the P-wave velocity and the wavelet transform multi-resolution analysis (WT-MRA). The WT-MRA method can unfold information within the frequency domain via decomposing the P-wave velocity. This enables us to extract and amplify hidden information embedded in the signal. Using Biot's theory, WT-MRA decomposition results can be divided into contributions from the pore-fluid and the rock framework. Therefore, I proposed a pore-pressure prediction model which is based on the pore-fluid contribution, calculated through WT-MRA, to the P-wave velocity.Open Acces

Detection and classification of vibrating objects in SAR images

The vibratory response of buildings and machines contains key information that can be exploited to infer their operating conditions and to diagnose failures. Furthermore, since vibration signatures observed from the exterior surfaces of structures are intrinsically linked to the type of machinery operating inside of them, the ability to monitor vibrations remotely can enable the detection and identification of the machinery. This dissertation focuses on developing novel techniques for the detection and M-ary classification of vibrating objects in SAR images. The work performed in this dissertation is conducted around three central claims. First, the non-linear transformation that the micro-Doppler return of a vibrating object suffers through SAR sensing does not destroy its information. Second, the instantaneous frequency (IF) of the SAR signal has sufficient information to characterize vibrating objects. Third, it is possible to develop a detection model that encompasses multiple scenarios including both mono-component and multi-component vibrating objects immersed in noise and clutter. In order to cement these claims, two different detection and classification methodologies are investigated. The first methodology is data-driven and utilizes features extracted with the help of the discrete fractional Fourier transform (DFRFT) to feed machine-learning algorithms (MLAs). Specifically, the DFRFT is applied to the IF of the slow-time SAR data, which is reconstructed using techniques of time-frequency analysis. The second methodology is model-based and employs a probabilistic model of the SAR slow-time signal, the Karhunen-Loève transform (KLT), and a likelihood-based decision function. The performance of the two proposed methodologies is characterized using simulated data as well as real SAR data. The suitability of SAR for sensing vibrations is demonstrated by showing that the separability of different classes of vibrating objects is preserved even after non-linear SAR processing Finally, the proposed algorithms are studied when the range-compressed phase-history data is contaminated with noise and clutter. The results show that the proposed methodologies yields reliable results for signal-to-noise ratios (SNRs) and signal-to-clutter ratios (SCRs) greater than -5 dB. This requirement is relaxed to SNRs and SCRs greater than -10 dB when the range-compressed phase-history data is pre-processed with the Hankel rank reduction (HRR) clutter-suppression technique

Quantum and classical correlations of multiply scattered light

Multiple scattering is a very common phenomenon since it occurs any time a wave meets a disordered medium. As almost any natural object has random structure in one form or another, the variety of the processes involving multiple scattering spans from electronic transport in solids to propagation of sound in a forest. In principle, multiple scattering is completely deterministic, and in the absence of absorption also reversible, which means that the information encoded into the incident wave can be perfectly recovered. However, in practice, due to its extreme complexity we often consider this process to be random, which leads to information loss. Within this approach correlations can be an important instrument of information recovery, because they directly quantify the amount of knowledge we get about the wave in a particular point from the measurement performed in a different point. In the first part of this thesis we study a novel type of mesoscopic correlations between the light intensities at the opposite sides of an opaque scattering slab. We study its dependence on the scattering medium properties and the incoming light beam parameters. In the last chapter of the first part we show how this correlation can be used to retrieve non-invasively the information about the shape of an object placed behind the scattering medium. In the second part we switch to the quantum aspects of the light propagation inside the scattering materials. We show that certain class of quantum correlations, quantum discord, can be present in the multimode output state of the scattered light even when the input light is in a thermal state, which is commonly considered classical. We propose a non-classicality measure based on the strength of this correlation, applying it to characterize the advantage due to the quantum measurement in discrimination of two coherent states in their mixture.Engineering and Physical Sciences Research Council (EPSRC

The use of late time response for stand off onbody concealed weapon detection

A new system for remote detection of onbody concealed weapons such as knives and handheld guns at standoff distances presented in this thesis. The system was designed, simulated, constructed and tested in the laboratory. The detection system uses an Ultrawide Band (UWB) antenna to bombard the target with a UWB electromagnetic pulse. This incident pulse induces electrical currents in the surface of an object such as a knife, which given appropriate conditions these currents generate an electromagnetic backscatter radiation. The radiated waves are detected using another UWB antenna to obtain the Late Time Response (LTR) signature of the detected object. The LTR signature was analysed using the Continuous Wavelet Transform (CWT) in order to assess the nature and the geometry of the object. The thesis presents the work which divided into two related areas. The first involved the design, simulation, fabrication, and testing of an Ultra-wide Band (UWB) antenna with operating bandwidth of 0.25 – 3.0 GHz and specific characteristics. Simulated and measured results show that the designed antenna achieves the design objectives which are, flat gain, a VSWR of around unity and distortion less transmitted narrow pulse. The operating bandwidth was chosen to cover the fundamental Complex Natural Resonance (CNR) modes of most firearms and to give a fine enough time resolution. The second area covered by this thesis presents a new approach for extract target signature based on the Continuous Wavelet Transform (CWT) applied to the scattering response of onbody concealed weapons. A series of experiments were conducted to test the operation of the detection system which involved onbody and offbody objects such as, knives, handheld guns, and a number of metallic wires of various dimensions. Practical and simulation results were in good agreement demonstrating the success of the approach of using the CWT in analyzing the LTR signature which is used for the first time in this work. Spectral response for every target could be seen as a distribution in which the energy level and life-time depended on the target material and geometry. The spectral density provides very powerful information concerning target unique signature

Dynamical nuclear spin polarization in a quantum dot with an electron spin driven by electric dipole spin resonance

We analyze the polarization of nuclear spins in a quantum dot induced by a single-electron spin that is electrically driven to perform coherent Rabi oscillations. We derive the associated nuclear-spin polarization rate and analyze its dependence on the accessible control parameters, especially the detuning of the driving frequency from the electron Larmor frequency. The arising nuclear-spin polarization is related to the Hartmann-Hahn effect known from the NMR literature with two important differences. First, in quantum dots one typically uses a micro magnet, leading to a small deflection of the quantization axes of the electron and nuclear spins. Second, the electric driving wiggles the electron with respect to the atomic lattice. The two effects, absent in the traditional Hartmann-Hahn scenario, give rise to two mechanisms of nuclear-spin polarization in gated quantum dots. The arising nuclear-spin polarization is a resonance phenomenon, achieving maximal efficiency at the resonance of the electron Rabi and nuclear Larmor frequency (typically a few or a few tens of MHz). As a function of the driving frequency, the polarization rate can develop sharp peaks and reach large values at them. Since the nuclear polarization is experimentally detected as changes of the electron Larmor frequency, we often convert the former to the latter in our formulas and figures. In these units, the polarization can reach hundreds of MHz/s in GaAs quantum dots and at least tens of kHz/s in Si quantum dots. We analyze possibilities to exploit the resonant polarization effects for achieving large nuclear polarization and for stabilizing the Overhauser field through feedback.Comment: 34 pages including 15 pages of appendices and 3 pages of references, 13 figures. In going from version v1 to v2, we have added Appendix J and K, and included minor changes stemming from the refereeing and proofs at Physical Review

Consequences of interactions in quantum Hall edge channels

The topic of electron quantum optics has recently assumed a prominent role in the condensed matter agenda. It aims at generating, manipulating and detecting individual electronic wave-packets ballistically propagating in mesoscopic devices to realize quantum-optical like experiments and set-ups in solid state devices. One of the main open problems in this field is the real time detection of the signal, which is a challenge for nowadays electronics. For this reason, techniques based on finite frequency current noise have been developed in order to reconstruct the time behavior of the signals. In this direction, a deep knowledge of quantum noise is needed in order to properly understand and control the time evolution of wave-packets. Moreover, one of the main differences between conventional quantum optics and electron quantum optics is represented by the fact that electrons are charged interacting particles. This leads to many-body effects which strongly affect the dynamics of excitations and play a major role in various experimental situations. The main purpose of this Thesis is to understand what are the consequences of unavoidable electronic interactions in edge channels of the quantum Hall effect, both in the integer and fractional regimes, on current-current fluctuations (i.e. noise). In particular, we have investigated: - the Hong-Ou-Mandel interferometry in a quantum Hall system at filling factor two, namely the physics of colliding identical excitations. Here, we have shown that the injected electronic wave-packets fractionalize before partitioning at a quantum point contact due to interactions. In addition, we have proposed a measurement protocol to determine the strength of interactions; - the peculiar quantum properties of the microwave radiation emitted by a quantum Hall device at filling factor two in presence of interactions. We have connected the squeezing of the emitted radiation to the current fluctuations comparing two different periodic drives. We have observed that a periodic train of Lorentzian pulses is characterized by a robust squeezing effect even in presence of interaction; - the noise associated to the current flowing between two different fractional quantum Hall edge states, with filling factors belonging to the Laughlin sequence, coupled through a quantum point contact and connected to two reservoirs placed at different temperatures. This noise contribution, known in literature as delta-T noise, is currently subject of an intense research from both the theoretical and the experimental point of view

Riesz-projection-based methods for the numerical simulation of resonance phenomena in nanophotonics

Resonance effects are ubiquitous in physics and essential for understanding wave propagation and interference. In the field of nanophotonics, devices are often based on the strong confinement of light by resonances. The numerical simulation of resonances plays a crucial role for the design and optimization of the devices. The resonances are electromagnetic field solutions to the time-harmonic source-free Maxwell's equations with loss mechanisms. The corresponding eigenproblems are non-Hermitian due to the losses leading to complex-valued eigenvalues. The material dispersion, which is typically significant in nanophotonics, results in nonlinear eigenproblems. In this thesis, we develop an approach based on Riesz projections for the expansion of electromagnetic fields caused by light sources into resonances. The Riesz projection expansion is computed by contour integration in the complex frequency plane. The numerical realization essentially relies on solving Maxwell's equations with a source term, meaning solving linear systems of equations. For this, Maxwell's equations are directly evaluated at the given frequencies on the integration contours, which implies that linearization of the corresponding nonlinear eigenproblems is not required. This makes Riesz-projection-based approaches a natural choice for dealing with eigenproblems from the field of nanophotonics. We further extend the Riesz projection expansion approach to optical far-field quantities, which is not straightforward due to the spatial divergence of the resonances with increasing distance from the underlying resonators. Based on the ideas of the Riesz projection expansion, we introduce approaches for the calculation of physically relevant eigenvalues and for computing eigenvalue sensitivities. Physically relevant means that the eigenvalues are significant with respect to the resonance expansion of the physical observable of interest. By using physical solutions to Maxwell's equations for the contour integration, the developed numerical methods have a strong relation to physics. The methods can be applied to any material system and to any measurable physical quantity that can be derived from the electric field. We apply the numerical methods to several recent nanophotonic applications, for example, single-photon sources from the field of quantum technology, plasmonic nanostructures characterized by nonlocal material properties, and nanoantennas based on bound states in the continuum. The approaches introduced in this thesis are developed for nanophotonic systems, but can be applied to any resonance problem.Resonanzeffekte treten in allen physikalischen Systemen auf, die durch Wellen beschrieben werden, und sie sind für die Beschreibung von Wellenausbreitung und Interferenz unerlässlich. Auf dem Gebiet der Nanophotonik basieren viele Geräte auf den durch Lichtquellen angeregten Resonanzen mit ihren stark erhöhten elektromagnetischen Feldern. Die numerische Simulation von Resonanzen ist ein wichtiges Hilfsmittel für die Entwicklung und Optimierung der Geräte. Die Resonanzen sind die Lösungen der zeitharmonischen quellenfreien Maxwell-Gleichungen mit Verlustmechanismen. Die entsprechenden Eigenwertprobleme sind aufgrund der Verluste nicht-Hermitesch, was zu komplexwertigen Eigenwerten führt. Die Materialdispersion, die in der Nanophotonik typischerweise signifikant ist, führt zu nichtlinearen Eigenwertproblemen. In dieser Dissertation entwickeln wir einen auf der Riesz-Projektion basierenden Ansatz für die Expansion von elektromagnetischen Feldern, die von Lichtquellen erzeugt werden, in Resonanzen. Wir berechnen die Riesz-Projektionen durch Konturintegration in der komplexen Frequenzebene. Die numerische Realisierung basiert im Wesentlichen auf der Lösung der Maxwell-Gleichungen mit einem Quellterm, das heißt der Lösung von linearen Gleichungssystemen. Dabei werden die Maxwell-Gleichungen direkt bei den gegebenen Frequenzen auf den Integrationskonturen ausgewertet, sodass eine Linearisierung der entsprechenden nichtlinearen Eigenwertprobleme nicht erforderlich ist. Das macht die auf der Riesz-Projektion basierenden Methoden zu einer natürlichen Wahl für die Behandlung von Eigenwertproblemen aus dem Bereich der Nanophotonik. Wir erweitern den Ansatz der Riesz-Projektions-Expansion auf optische Größen im Fernfeld, was aufgrund der räumlichen Divergenz der Resonanzen mit zunehmender Entfernung von den zugrunde liegenden Resonatoren problematisch ist. Basierend auf den Ideen der Riesz-Projektions-Expansion entwickeln wir außerdem Methoden zur Berechnung physikalisch relevanter Eigenwerte und zur Berechnung von Sensitivitäten von Eigenwerten. Physikalisch relevant bedeutet, dass die Eigenwerte in Bezug auf die Resonanzexpansion der interessierenden physikalischen Größe signifikant sind. Durch die Verwendung physikalischer Lösungen der Maxwell-Gleichungen für die Konturintegration haben die entwickelten numerischen Methoden einen starken Bezug zur zugrunde liegenden Physik. Die Methoden können auf jedes Materialsystem und auf jede messbare physikalische Größe angewendet werden, die sich aus dem elektrischen Feld herleiten lässt. Wir wenden die numerischen Methoden auf mehrere aktuelle nanophotonische Strukturen an, wie zum Beispiel Einzelphotonenquellen aus dem Bereich der Quantentechnologie, plasmonische Nanostrukturen, die sich durch nichtlokale Materialeigenschaften auszeichnen, und Nanoantennen, die auf gebundenen Zuständen im Kontinuum basieren. Die in dieser Dissertation vorgestellten Ansätze werden für nanophotonische Systeme entwickelt, lassen sich aber auf jedes Resonanzproblem anwenden

Holistic methods for visual navigation of mobile robots in outdoor environments

Differt D. Holistic methods for visual navigation of mobile robots in outdoor environments. Bielefeld: Universität Bielefeld; 2017