This report analyzes the difference between discriminative and generative image classifiers when tested on noise. The generative classifier was a maximum-likelihood based classifier using a normalizing flow as the generative model. In this work, a coupling flow such as RealNVP was used. For the discriminative classifier a convolutional network was implemented. A detailed description of how these classifiers were implemented is given in the report. The report shows how this generative classifier outperforms the discriminative classifier when tested on adversarial noise. However, tests are also conducted on salt and pepper noise and Gaussian noise, here the results show that the generative classifier gets outperformed by the discriminative classifier. Tests were also conducted on Gaussian noise once both classifiers had been trained on Gaussian noise, the results from these tests show that the discriminative classifier performs significantly better once trained on Gaussian noise. However, the generative classifier does only show marginal increases in performance and performs worse on clean data once trained on Gaussian noise. / Den här rapporten analyserar skillnaden mellan diskriminativa och generativa modellklasser för bildigenkänning när de testas på brus. Den generativa modellklassen var en maximum-likelihood baserad generativ klassifikationsmodell. Inom detta arbete användes kopplingsflödet RealNVP. För den diskriminativa bildigenkänningsmodellen så implementerades ett faltningsnätverk. En detaljerad beskrivning för hur dessa bildigenkänningsmodeller genomfördes är given i rapporten. Rapporten visar hur den generativa modellklassen överträffar den diskriminativa modellklassen när de testas på adversarialt brus. Testerna utförs emellertid med salt och peppar brus och Gaussiskt brus, för dessa visar resultaten att den generativa modellklassen överträffas av den diskriminativa modellklassen. Den generativa modellklassen visar emellertid endast marginella ökningar i prestanda, och har en sämre prestanda på ren data efter att den tränats på Gaussiskt brus. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

In the Thesis, linear stochastic differential equations in a Hilbert space driven by a cylindrical fractional Brownian motion with the Hurst parameter in the interval H < 1/2 are considered. Under the conditions on the range of the diffusion coefficient, existence of the mild solution is proved together with measurability and continuity. Existence of a limiting distribution is shown for exponentially stable semigroups. The theory is modified for the case of analytical semigroups. In this case, the conditions for the diffusion coefficient are weakened. The scope of the theory is illustrated on the Heath-Jarrow-Morton model, the wave equation, and the heat equation. 1

Image De-noising forms an integral part of image processing. It is used as a standalone algorithm for improving the quality of the image obtained through camera as well as a starting stage for image processing applications like face recognition, super resolution etc. Non Local Means (NL-Means) and Bilateral Filter are two computationally complex de-noising algorithms which could provide good de-noising results. Due to its computational complexity, the real time applications associated with these letters are limited. In this thesis, we propose the use of hardware accelerators such as GPU (Graphics Processing Units) and FPGA (Field Programmable Gate Arrays) to speed up the filter execution and efficiently implement using them. GPU based implementation of these letters is carried out using Open Computing Language (Open CL). The basic objective of this research is to perform high speed de-noising without compromising on the quality. Here we implement a basic NL-Means filter, a Fast NL-Means filter, and Bilateral filter using Gauss Polynomial decomposition on GPU. We also propose a modification to the existing NL-Means algorithm and Gauss Polynomial Bilateral filter. Instead of Gaussian Spatial Kernel used in standard algorithm, Box Spatial kernel is introduced to improve the speed of execution of the algorithm. This research work is a step forward towards making the real time implementation of these algorithms possible. It has been found from results that the NL-Means implementation on GPU using Open CL is about 25x faster than regular CPU based implementation for larger images (1024x1024). For Fast NL-Means, GPU based implementation is about 90x faster than CPU implementation. Even with the improved execution time, the embedded system application of the NL-Means is limited due to the power and thermal restrictions of the GPU device. In order to create a low power and faster implementation, we have implemented the algorithm on FPGA. FPGAs are reconfigurable devices and enable us to create a custom architecture for the parallel execution of the algorithm. It was found that the execution time for smaller images (256x256) is about 200x faster than CPU implementation and about 25x faster than GPU execution. Moreover the power requirements of the FPGA design of the algorithm (0.53W) is much less compared to CPU(30W) and GPU(200W).

Tato diplomová práce je zaměřena na analýzu chování magnetopiezoelastického kmitajícího nosníku. V teoretické části jsou odvozeny diskretizované parametry, které popisují reálnou soustavu jako model s jedním stupněm volnosti. Tento model je následně použit pro kvalitativní i kvantitativní analýzu chování tohoto harvesteru. Frekvenční odezva harmonicky buzeného systému je zkoumána v dvouparametrické nebo tříparametrické analýze v závislosti na amplitudě buzení, elektrické zátěži a vzdálenosti mezi magnety. Posledně zmíněný parametr je v práci tím hlavním, proto je vliv vzdálenosti magnetů zkoumán také s pomocí bifurkačních diagramů. Tyto diagramy byly navíc použity k vytvoření oscilační "mapy", která pro každé zatěžovací podmínky ukazuje, jakou vzdálenost magnetů je třeba nastavit, aby bylo generováno nejvíce energie. Práce je doplněna o ukázky několika jevů, které mohou značně ovlivnit chování systému, pokud se nejdená o čistě harmonické buzení.

Vehicles losing their GPS signal is a considerable issue for autonomous vehicles and can be a danger to people in their vicinity. To circumvent this issue, a particle filter localization technique using pre-generated offline Open Street Map (OSM) maps was investigated in a software simulation of Scania’s heavy-duty trucks. The localization technique runs in real-time and provides a way to localize the vehicle safely if the starting position is known. Access to global localization was limited, and the particle filter still succeeded in localizing the vehicle in the vicinity of the correct road segment by creating a graph of the map information and matching the trajectory to the vehicle’s sensor data. The mean error of the Particle filter localization technique in optimal conditions is 16m, which is 20% less than an optimally tuned dead reckoning solution. The mean error is about 50% larger compared to a Global Positioning System. The final product shows potential for expansion but requires more investigation to allow for real-world deployment. / Att fordon kan mista sin GPS-signal är ett stort problem för autonoma fordon och kan vara en fara för människor i dess närhet. För att undvika detta problem föreslås en icke-global lokaliseringsteknik som använder Open Street Maps-kartor (OSM) och ett partikelfilter för att lokalisera fordonet i en mjukvarusimulation. Implementering körs i realtid och anger fordonets position med en tillräcklig träffsäkerhet för att det inte ska utgöra någon fara om dess startposition är känd. Globala lokaliseringsmöjligheter var begränsade, och partikelfiltret lyckades lokalisera fordonet till rätt vägsegment genom att konstruera en graf över den kartinformation den läst in och para ihop fordonets nuvarande färdväg med denna. Resultatet ger en lösning som optimalt har ett medelfel på 16m, vilket är 20% mindre än medelfelet jämfört med optimiserad dödräkning. Lösningen har ca 50% större medelfel än positionering med GPS. Slutresultatet visar en potential att användas i verkliga situationer, men kräver mer undersökningar.

Approved for public release, distribution is unlimited / Orthogonal frequency division multiplexing (OFDM) is being successfully used in numerous applications. It was chosen for IEEE 802.11a wireless local area network (WLAN) standard, and it is being considered for the fourthgeneration mobile communication systems. Along with its many attractive features, OFDM has some principal drawbacks. Sensitivity to frequency errors is the most dominant of these drawbacks. In this thesis, the frequency offset and phase noise effects on OFDM based communication systems are investigated under a variety of channel conditions covering both indoor and outdoor environments. The simulation performance results of the OFDM system for these channels are presented. / Lieutenant Junior Grade, Turkish Navy

Die vorliegende Arbeit befasst sich mit dem Einfluss von nicht-weißem oder nicht-Gauß’schem synaptischen Rauschen auf die Informationsübertragung in stochastischen Neuronenmodellen. Ziel ist es, zu verstehen, wie eine Nervenzelle ein Signal in ihrer Pulsaktivität kodiert. Synaptisches Rauschen beschreibt hier den Einfluss anderer Nervenzellen, die nicht das interessierende Signal tragen, aber seine Übertragung durch ihre synaptische Wirkung auf die betrachtete Zelle beeinflussen. In stochastischen Neuronenmodellen wird diese Hintergrundaktivität durch einen stochastischen Prozess mit geeigneter Statistik beschrieben. Ist die Rate, mit der präsynaptische Pulse auftreten, hoch und zeitlich konstant, die Wirkung einzelner Pulse aber verschwindend gering, so wird das synaptische Rauschen durch einen Gauß’schen Prozess beschrieben. Oft wird zudem angenommen, dass das Rauschen unkorreliert (weiß) ist. In dieser Arbeit wird neuronale Signalübertragung in dem Fall untersucht, dass eine solche Näherung nicht mehr gerechtfertigt ist, d.h. wenn der synaptische Hintergrund durch einen stochastischen Prozess beschrieben werden muss, der nicht weiß, nicht Gauß’sch, oder weder weiß noch Gauß’sch ist. Mittels Simulationen und analytischer Rechnungen werden drei Szenarien behandelt: Zunächst betrachten wir eine Zelle, die nicht ein, sondern zwei Signale empfängt, welche zusätzlich durch synaptische Kurzzeitplastizität gefiltert werden. In diesem Fall muss der Hintergrund durch ein farbiges Rauschen beschrieben werden. Im zweiten Szenario betrachten wir den Fall, dass der Effekt einzelner Pulse nicht mehr als schwach angenommen werden kann. Das Rauschen ist dann nicht mehr Gauß’sch, sondern ein Schrotrauschen. Schließlich untersuchen wir den Einfluss einer präsynaptischen Population, deren Feuerrate nicht zeitlich konstant ist, sondern zwischen Phasen hoher und niedriger Aktivität, sogenannten up und down states, springt. In diesem Fall ist das Rauschen weder weiß noch Gauß’sch. / This thesis is concerned with the effect of non-white or non-Gaussian synaptic noise on the information transmission properties of single neurons. Synaptic noise subsumes the massive input that a cell receives from thousands of other neurons. In the framework of stochastic neuron models, this input is described by a stochastic process with suitably chosen statistics. If the overall arrival rate of presynaptic action potentials is high and constant in time and if each individual incoming spike has only a small effect on the dynamics of the cell, the massive synaptic input can be modeled as a Gaussian process. For mathematical tractability, one often assumes that furthermore, the input is devoid of temporal structure, i.e. that it is well described by a Gaussian white noise. This is the so-called diffusion approximation (DA). The present thesis explores neuronal signal transmission when the conditions that underlie the DA are no longer met, i.e. when one must describe the synaptic background activity by a stochastic process that is not white, not Gaussian, or neither. We explore three distinct scenarios by means of simulations and analytical calculations: First, we study a cell that receives not one but two signals, additionally filtered by synaptic short-term plasticity (STP), so that the background has to be described by a colored noise. The second scenario deals with synaptic weights that cannot be considered small; here, the effective noise is no longer Gaussian and the shot-noise nature of the input has to be taken into account. Finally, we study the effect of a presynaptic population that does not fire at a rate which is constant in time but instead undergoes transitions between states of high and low activity, so-called up and down states.

We implement a package for the construction of a new class of Low Density Parity Check (LDPC) codes based on a new random high girth graph construction technique, and study the performance of the codes so constructed on both the Additive White Gaussian Noise (AWGN) channel as well as the Binary Erasure Channel (BEC). Our codes are “near regular”, meaning thereby that the the left degree of any node in the Tanner graph constructed varies by at most 1 from the average left degree and so also the right degree. The simulations for rate half codes indicate that the codes perform better than both the regular Progressive Edge Growth (PEG) codes which are constructed using a similar random technique, as well as the MacKay random codes. For high rates the ARG (Almost Regular high Girth) codes perform better than the PEG codes at low to medium SNR’s but the PEG codes seem to do better at high SNR’s. We have tried to track both near codewords as well as small weight codewords for these codes to examine the performance at high rates. For the binary erasure channel the performance of the ARG codes is better than that of the PEG codes. We have also proposed a modification of the sum-product decoding algorithm, where a quantity called the “node credibility” is used to appropriately process messages to check nodes. This technique substantially reduces the error rates at signal to noise ratios of 2.5dB and beyond for the codes experimented on. The average number of iterations to achieve this improved performance is practically the same as that for the traditional sum-product algorithm.

This work is focused on the subject of the interference modelling for xDSL technologies. First, the xDSL technologies are explained. Following is the presentation and description of the different kinds of the xDSL technologies. The next part deals with the basic parameters of metallic cable lines – especially the primary and secondary parameters. Nowadays wider bandwidths are used for the achievement of higher data transmission rates. During a higher frequency signal transmission a more intensive line attenuation appears. To identify the transfer characteristics of the lines while using an xDSL system, mathematic models of transmission lines are applied. That is why these mathematic models are dealt with in the next chapter. At the end of this section the mathematic models are compared using the modular and phase characteristics. The main aim of the work is to describe the different impacts which influence the efficiency of the xDSL systems. First, the causes interfering from the inside of the cable are deeply explained: Near End Crosstalk (NEXT), Far End Crosstalk (FEXT), Additive White Gaussian Noise (AWGN). Following is the explanation of the external interfering impacts: Radio Frequency Interference (RFI) and Impulse Noise. The next goal of this thesis is a design of a workstation for the tests of spectral features and the efficiency of the xDSL systems. The work also presents a designed GUI application and its description. The GUI application is an instrument for the choice or data entry of the final interference. The last chapter describes a realization of a measurement and shows the measured characteristics which were recorded on the ADSL tester and oscilloscope.

The thesis concerns the problem of interference modelling for xDSL technologies and Ethernet. The introduction describes the origin of crosstalk, that arise during the operation of the systems and the physical properties of the lines, therefore, the next section describes the properties of the primary and secondary parameters of the homogenous line and their modelling. In order to achieve higher data rates on the metallic line, systems with larger frequency spectrum are applied, resulting in a greater attenuation of the line. This issue and the characteristics determination of the transmission systems are subjects of the mathematical models, which are divided according to the modelling of primary or secondary parameters. The main goal of this work is to describe the effects which influence the performance of data transfer via xDSL and Ethernet technology focusing on internal and external disturbances acting on the cable lines. This is the crosstalk at the near and far end, adaptive white noise, radio frequency interference RFI and impulse noise. Following part of the thesis deals with the properties of xDSL technologies, specifically ADSL2+ and VDSL2 and Ethernet. Another aim is to design applications which enable to test the performance of xDSL and Ethernet transmission systems with its own award simulations interference. The conclusion describes the design and implementation of laboratory experiments for measuring of the efficiency and spectral properties of xDSL. The proposed laboratory protocols are annexed to this thesis, including the measured waveforms.