As technology has advanced, data has become more and more important. The more breakthroughs are achieved, the more data is needed to support them. As a result, more storage is required in the system's memory. Compression is therefore required. Before it can be stored, the data must be compressed. To ensure that information is not lost, efficient compression is necessary. This also makes sure that there is no redundancy in the data that is being kept and stored. Compressive sensing has emerged as a new field of compression thanks to developments in sparse optimization. Rather than relying just on compression and sensing formulations, the theory blends the two. The objective of this thesis is to analyze the concept of compressive sensing and to study several reconstruction algorithms. Additionally, a few of the algorithms were put into practice. This thesis also included a model of the ECG, which is vital in determining the health of the heart. For the most part, the ECG is utilized to diagnose heart illness, and a modified synthetic ECG can be used to mimic some of these arrhythmias.

Students at Uppsala University have for some years been given the opportunity to take courses in subjects directly, or indirectly, related to the fields of signal processing and signal analysis. According to the directors of these courses, a considerable number of students are recurringly having difficulties grasping different concepts related to this field of study. This report covers a tool that easily allows teachers to visualize and listen to different manipulations of signals, which should help students get an intuitive understanding of the subject. Features of the system include multiple kinds of analog filters, sampling with variable settings and zero-order hold reconstruction. The finished system is flexible, tunable and modifiable to the teachers every need, making it usable for a wide variety of courses involving signal processing. The system meets its requirements even though individual components’ results de- viate slightly from ideal values. / Studenter vid Uppsala Universitet har, under ett antal år, givits möjligheten att läsa kurser inom ämnen direkt, eller indirekt, relaterade till signalbehandling/signalanalys. Enligt kursansvariga för dessa kurser har en ansenlig andel av studenterna svårigheter med att förstå en del av de begrepp och fenomen som förekommer under kurserna. Denna rapport behandlar ett verktyg som ger lärare i dessa kurser möjlighet att på ett enkelt sätt visualisera och lyssna på olika manipulationer av signaler, vilket bör hjälpa studenterna bygga en intuition för ämnet. Systemets olika funktioner inkluderar flera olika typer av analoga filter, sampling med olika inställningar, och så kallad ’Zero-Order-Hold’ rekonstruktion. Det resulterande systemet är flexibelt, inställbart och modifierbart till användarens behov, vilket gör det applicerbart i flera kurser som innefattar signalbehandling/analys. Systemet möter kraven som ställs, även fast resultaten hos individuella komponenter avviker aningen från ideala värden.

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

International Telemetering Conference Proceedings / October 30-November 02, 1995 / Riviera Hotel, Las Vegas, Nevada / In this paper, a new concept in PCM telemetry encoding equipment is described. Existing "programmable" PCM encoders allow only simple changes in the functionality of the hardware, such as input gain, offset, and word formatting. More importantly, these encoders do not provide capability for "in-flight" processing of signals and in general have not taken advantage of existing hardware and software digital signal processing technology. In-flight processing of signals can provide a significant reduction in the required transmission bandwidth, allowing additional data that may not have otherwise been transmitted to be sent on the telemetry channel. A modular digital signal processor (DSP) based PCM encoder architecture is described that has a set of on-board processing algorithms configurable via a simple-to-use graphical user interface. Algorithms included are compression (lossy and lossless), Fourier transforms of various resolutions (typically followed by peak detection to provide a data rate reduction), extreme values (max, min, rms), time filtering, regression, trajectory prediction, and serial data stream processing. Custom algorithms can be developed and included as part of the suite of processing algorithms. The preprocessing algorithms exist as firmware on the DSPs and can accommodate as many different signals as the processing bandwidth of the DSP can handle. Typically one DSP can handle many input signals and different algorithms. The encoder is programmable via a standard RS-232 serial interface allowing the signal input configuration, telemetry frame layout, and on-board processing algorithms to be changed quickly.

Die Schallausbreitung in der Atmosphäre wird durch vertikale Gradienten meteorologischer Größen, insbesondere Lufttemperatur und Windvektor, maßgeblich beeinflusst. Ziel dieser Studie ist die Abschätzung des Einflusses einer Schallstrahlenrefraktion infolge von Temperatur- und Windgradienten auf die Laufzeit akustischer Signale zwischen Sendern und Empfängern. Mit Hilfe des hier vorgestellten Schallstrahlenmodells SMART (Sound propagation model of the atmosphere using ray-tracing) wird die Differenz der Laufzeiten entlang des gekrümmten Schallweges (mit Refraktion) und entlang der geraden Verbindungslinie (ohne Refraktion) zwischen einem Sender und einem Empfänger berechnet. Je größer die Sender-Empfänger-Entfernung und je größer der Unterschied zwischen Sender- und Empfängerhöhe sind, desto größer sind auch die Beträge der Laufzeitunterschiede. Der gekoppelte Einfluss von Temperatur- und Windprofil auf die Schallstrahlenrefraktion lässt zum großen Teil jedoch keine pauschalen Abschätzungen der Laufzeitdifferenz zu. Die erzielten Untersuchungsergebnisse werden insbesondere für eine Einschätzung der Anwendbarkeit einer Schallstrahlapproximation (geradlinige Schallstrahlen) bei der akustischen Laufzeittomographie benötigt. / Sound propagation inside the atmosphere is mainly influenced by vertical gradients of meteorological quantities, in particular air temperature and wind vector. The aim of this study is to estimate the influence of the sound ray refraction on the travel time of acoustic signals between transmitters and receivers due to temperature and wind gradients. The difference of the travel times along the curved sound ray (with refraction) and along the straight line (without refraction) between the transmitter and the receiver is calculated by means of the presented sound-ray model SMART (Sound propagation model of the atmosphere using ray-tracing). The greater the transmitter-receiver-distances, and the greater the height-level differences of transmitter and receiver, the greater are the travel-time differences. However, the coupled influence of temperature and wind profiles on the sound-ray refraction does mostly not allow an universal estimation of the travel-time difference. The obtained results are necessary to validate the sound-ray approximation (straight-line approximation) applied by the acoustic tomography.

QC 351 A7 no. 65 / The significance of signal-dependent noise is discussed. Particular emphasis is placed on the type of multiplicative noise present in the density variations in a photographic emulsion. A theoretical treatment of the effect of multiplicative noise on signal detection and signal discrimination problems is presented. Optimum test statistics are derived for processing a sampled message to detect the presence of a known signal. Multiplicative noise described by Poisson and Gaussian statistics is considered. The expressions are extended to include the two-signal discrimination problem. Two-dimensional signal fields in the presence of multiplicative noise are simulated in a computer and processed for optimum signal detection according to the two derived methods. These results are compared to the results of processing based on the assumption of stationary noise statistics. This comparison reveals that modest improvements (20% to 30% reduction in false alarm rate) are obtained when the signal-dependent nature of the noise statistics is considered. The effects of signal-to-noise ratio, signal structure, and changing background level are also investigated. An example of optimum signal discrimination using circles and squares as signals in multiplicative noise is reported. An improvement in the percentage of correctly identified signals is again observed when the proper test statistic is used. Two examples of signal filtering in the presence of signal-dependent noise are included. The first concerns the processing of a real star field to determine the location of weak stars. The second is an illustration of the signal information contained in the noise spectrum of a message recorded on a common photographic film.

Large-scale networks are becoming more prevalent, with applications in healthcare systems, financial networks, social networks, and traffic systems. The detection of normal and abnormal behaviors (signals) in these systems presents a challenging problem. State-of-the-art approaches such as principal component analysis and graph signal processing address this problem using signal projections onto a space determined by an eigendecomposition or singular value decomposition. When a graph is directed, however, applying methods based on the graph Laplacian or singular value decomposition causes information from unidirectional edges to be lost. Here we present a novel formulation and graph signal processing framework that addresses this issue and that is well suited for application to extremely large, directed, sparse networks. In this thesis, we develop and demonstrate a graph Fourier transform for which the spectral components are the Jordan subspaces of the adjacency matrix. In addition to admitting a generalized Parseval’s identity, this transform yields graph equivalence classes that can simplify the computation of the graph Fourier transform over certain networks. Exploration of these equivalence classes provides the intuition for an inexact graph Fourier transform method that dramatically reduces computation time over real-world networks with nontrivial Jordan subspaces. We apply our inexact method to four years of New York City taxi trajectories (61 GB after preprocessing) over the NYC road network (6,400 nodes, 14,000 directed edges). We discuss optimization strategies that reduce the computation time of taxi trajectories from raw data by orders of magnitude: from 3,000 days to less than one day. Our method yields a fine-grained analysis that pinpoints the same locations as the original method while reducing computation time and decreasing energy dispersal among spectral components. This capability to rapidly reduce raw traffic data to meaningful features has important ramifications for city planning and emergency vehicle routing.

Signal transduction via the phosphoinositide (PI) second messenger system has key roles in the development and plasticity of the neocortex. The present study localized PI responses to individual cortical layers in slices of developing rat somatosensory cortex. The acetylcholine agonist carbachol and the glutamate agonist trans-1-amino-1,3-cyclopentanedicarboxylic acid (ACPD) were used to stimulate PI turnover. The PI responses were compared to the distribution of the corresponding PI-linked receptors in order to investigate the regional ontogeny of PI coupling to receptors in relation to neural development. The method for assessing PI turnover was modified from Hwang et al. (1990). This method images the PI response autoradiographically through the localizaton of [3H]cytidine that has been incorporated into the membrane-bound intermediate, cytidine diphosphate diacylglycerol. In each age group (postnatal days 4-30), carbachol resulted in more overall labeling than ACPD. For both agonists, the response peaked on postnatal day 10 (P10) and was lowest in the oldest age group. The laminar distribution of the carbachol PI response from P4-P16 corresponded fairly well with the laminar distribution of [3H]quinuclidinyl benzilate binding (Fuchs, 1995). However, in the subplate layer the carbachol response was strong while receptor binding was minimal. The carbachol response decreased after postnatal day 10, while the overall levels of receptor binding continued to increase. From P5 - P14, PI-linked metabotropic glutamate receptors are most concentrated in layer IV (Blue et al., 1997), whereas only on P6 was there a correspondingly high ACPD-initiated PI response in this layer. Unlike receptors, the PI response was strong in upper V (P4 - P12) and within layers II/III (P8 - P16). From P4 - P21, the subplate showed relatively high PI labeling compared to receptor binding. The several differences between the distribution of PI response and receptors suggest spatiotemporal heterogeneity of receptor coupling to second messenger systems.

De nombreuses applications de traitement de signal nécessitent la connaissance de la matrice de covariance des données reçues. Lorsqu'elle n'est pas directement accessible, elle est estimée préalablement à l'aide de données d'apprentissage. Traditionnellement, le milieu est considéré comme gaussien. L'estimateur du maximum de vraisemblance est alors la sample covariance matrix (SCM). Cependant, dans de nombreuses applications, notamment avec l'arrivée des techniques haute résolution, cette hypothèse n'est plus valable. De plus, même en milieu gaussien, il s'avère que la SCM peut-être très influencée par des perturbations (données aberrantes, données manquantes, brouilleurs...) sur les données. Dans cette thèse nous nous proposons de considérer un modèle plus général, celui des distributions elliptiques. Elles permettent de représenter de nombreuses distributions et des campagnes de mesures ont montré leur bonne adéquation avec les données réelles, dans de nombreuses applications telles que le radar ou l'imagerie hyperspectrale. Dans ce contexte, nous proposons des estimateurs plus robustes et plus adaptés : les M-estimateurs et l'estimateur du point-fixe (FPE). Leurs performances et leur robustesse sont étudiées et comparées à celles de la SCM. Nous montrons ainsi que dans de nombreuses applications, ces estimateurs peuvent remplacer très simplement la SCM, avec de meilleures performances lorsque les données sont non-gaussiennes et des performances comparables à la SCM lorsque les données sont gaussiennes. Les résultats théoriques développés dans cette thèse sont ensuite illustrés à partir de simulations puis à partir de données réels dans le cadre de traitements spatio-temporels adaptatifs. / In many signal processing applications, the covariance matrix of the received data must be known. If unknown, it is firstly estimated with some training data. Classically, the background is considered as Gaussian. In such a case, the maximum likelihood estimator is the Sample Covariance Matrix (SCM). However, due to high resolution methods or other new technics, the Gaussian assumption is not valid anymore. Moreover, even when the data are Gaussian, the SCM can be strongly influenced by some disturbances such as missing data and/or outliers. In this thesis, we use a more general model which encompasses a large panel of distributions: the elliptical distributions. Many campagns of measurement have shown that this model leads to a better modelling of the data. In this context, we present more robust and adapted estimators: the M-estimators and Fixed Point Estimator (FPE). Their properties are derived in terms of performance and robustness, and they are compared to the SCM. We show that these estimators can be used instead of the SCM with nearly the same performance when the data are Gaussian, and better performance when the data are non-Gaussian. Theoretical results are emphasized on simulations and on real data in a context of Space Time Adaptive Processing.

Dans cette thèse, nous nous intéressons à des liens de transmission optique sans-fil utilisés dans un réseau de capteurs sous-marin. Dans un premier temps, nous étudions les propriétés optiques de l'eau de mer dans le but de définir les équations qui régissent la propagation des ondes optiques dans l'eau. Nous proposons d'utiliser le modèle d'Henyey-Greenstein à deux termes pour modéliser la diffusion d'angle et montrons qu'il décrit mieux la propagation d'ondes, comparé au modèle classique d'Henyey-Greenstein. Ensuite, nous caractérisons le canal optique sous-marin en nous basant sur des simulations de Monte Carlo et présentons la réponse impulsionnelle du canal pour différents paramètres d'émetteur-récepteur et de canal. Nous démontrons que, sauf dans le cas des eaux turbides, la dispersion temporelle du canal est négligeable sur des distances de quelques dizaines de mètres et pour des débits allant jusqu'à1Gbps. Dans un deuxième temps, nous nous intéressons aux problèmes liés à la mise en œuvre de tels liens. Nous commençons par étudier l'effet de désalignement entre l'émetteur et le récepteur, en particulier, en prenant en compte le champ de vue limité du récepteur. De plus, nous étudions le choix du photo-détecteur et aussi comparons les performances de différents schémas de modulation d'intensité en vue d'utilisation dans un système de communication optique sous-marin. Enfin, nous présentons une série des résultats que nous avons obtenus avec une maquette expérimentale dans une piscine pour valider une partie de nos résultats théoriques. / In this thesis, we consider optical wireless communication as a promising solution for high rate data transmission in power restricted underwater wireless sensor networks. A propagating light beam in seawater is subject to absorption and scattering due to the interaction with the particles within water. This practically limits the transmission range to a few tens of meters. In view of characterizing the underwater optical channel, we first study the inherent optical properties of the seawater and provide a model for underwater optical beam propagation. Concerning angle scattering, we propose to use the two-term Henyey-Greenstein model and show that it is more accurate than the commonly used Henyey-Greenstein model, especially in pure sea waters. Then, based on Monte Carlo simulations, we obtain the channel impulse response and quantify the channel time dispersion for different transmitter/receiver parameters and link distances. Through the numerical results that we present, we show that, except for highly turbid waters, the channel time dispersion can be neglected when working over moderate distances. Next, as a practical limitation, we focus on transmitter-receiver misalignment and evaluate its effect, in particular, by taking into account the limited receiver's field-of-view. Afterwards, we investigate the choice of the photo-detector, and furthermore contrast the performance of different intensity modulation techniques and discuss their suitability for use in the underwater optical communication system. Lastly, we provide a series of experimental measurement results that we have conducted inside a pool in order to validate a part of our theoretical studies.