Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Development of original analytical methods for the therapeutic drug monitoring of CNS druges: Antipsychotics, Antidepressants and Anxiolytics-hypnotics

Great strides have been made in the last few years in the pharmacological treatment of neuropsychiatric disorders, with the introduction into the therapy of several new and more efficient agents, which have improved the quality of life of many patients. Despite these advances, a large percentage of patients is still considered “non-responder” to the therapy, not drawing any benefits from it. Moreover, these patients have a peculiar therapeutic profile, due to the very frequent application of polypharmacy, attempting to obtain satisfactory remission of the multiple aspects of psychiatric syndromes. Therapy is heavily individualised and switching from one therapeutic agent to another is quite frequent. One of the main problems of this situation is the possibility of unwanted or unexpected pharmacological interactions, which can occur both during polypharmacy and during switching. Simultaneous administration of psychiatric drugs can easily lead to interactions if one of the administered compounds influences the metabolism of the others. Impaired CYP450 function due to inhibition of the enzyme is frequent. Other metabolic pathways, such as glucuronidation, can also be influenced. The Therapeutic Drug Monitoring (TDM) of psychotropic drugs is an important tool for treatment personalisation and optimisation. It deals with the determination of parent drugs and metabolites plasma levels, in order to monitor them over time and to compare these findings with clinical data. This allows establishing chemical-clinical correlations (such as those between administered dose and therapeutic and side effects), which are essential to obtain the maximum therapeutic efficacy, while minimising side and toxic effects. It is evident the importance of developing sensitive and selective analytical methods for the determination of the administered drugs and their main metabolites, in order to obtain reliable data that can correctly support clinical decisions. During the three years of Ph.D. program, some analytical methods based on HPLC have been developed, validated and successfully applied to the TDM of psychiatric patients undergoing treatment with drugs belonging to following classes: antipsychotics, antidepressants and anxiolytic-hypnotics. The biological matrices which have been processed were: blood, plasma, serum, saliva, urine, hair and rat brain. Among antipsychotics, both atypical and classical agents have been considered, such as haloperidol, chlorpromazine, clotiapine, loxapine, risperidone (and 9-hydroxyrisperidone), clozapine (as well as N-desmethylclozapine and clozapine N-oxide) and quetiapine. While the need for an accurate TDM of schizophrenic patients is being increasingly recognized by psychiatrists, only in the last few years the same attention is being paid to the TDM of depressed patients. This is leading to the acknowledgment that depression pharmacotherapy can greatly benefit from the accurate application of TDM. For this reason, the research activity has also been focused on first and second-generation antidepressant agents, like triciclic antidepressants, trazodone and m-chlorophenylpiperazine (m-cpp), paroxetine and its three main metabolites, venlafaxine and its active metabolite, and the most recent antidepressant introduced into the market, duloxetine. Among anxiolytics-hypnotics, benzodiazepines are very often involved in the pharmacotherapy of depression for the relief of anxious components; for this reason, it is useful to monitor these drugs, especially in cases of polypharmacy. The results obtained during these three years of Ph.D. program are reliable and the developed HPLC methods are suitable for the qualitative and quantitative determination of CNS drugs in biological fluids for TDM purposes.

Foetal heart rate recording: analysis and comparison of different methodologies

Monitoring foetal health is a very important task in clinical practice to appropriately plan pregnancy management and delivery. In the third trimester of pregnancy, ultrasound cardiotocography is the most employed diagnostic technique: foetal heart rate and uterine contractions signals are simultaneously recorded and analysed in order to ascertain foetal health. Because ultrasound cardiotocography interpretation still lacks of complete reliability, new parameters and methods of interpretation, or alternative methodologies, are necessary to further support physicians’ decisions. To this aim, in this thesis, foetal phonocardiography and electrocardiography are considered as different techniques. Further, variability of foetal heart rate is thoroughly studied. Frequency components and their modifications can be analysed by applying a time-frequency approach, for a distinct understanding of the spectral components and their change over time related to foetal reactions to internal and external stimuli (such as uterine contractions). Such modifications of the power spectrum can be a sign of autonomic nervous system reactions and therefore represent additional, objective information about foetal reactivity and health. However, some limits of ultrasonic cardiotocography still remain, such as in long-term foetal surveillance, which is often recommendable mainly in risky pregnancies. In these cases, the fully non-invasive acoustic recording, foetal phonocardiography, through maternal abdomen, represents a valuable alternative to the ultrasonic cardiotocography. Unfortunately, the so recorded foetal heart sound signal is heavily loaded by noise, thus the determination of the foetal heart rate raises serious signal processing issues. A new algorithm for foetal heart rate estimation from foetal phonocardiographic recordings is presented in this thesis. Different filtering and enhancement techniques, to enhance the first foetal heart sounds, were applied, so that different signal processing techniques were implemented, evaluated and compared, by identifying the strategy characterized on average by the best results. In particular, phonocardiographic signals were recorded simultaneously to ultrasonic cardiotocographic signals in order to compare the two foetal heart rate series (the one estimated by the developed algorithm and the other provided by cardiotocographic device). The algorithm performances were tested on phonocardiographic signals recorded on pregnant women, showing reliable foetal heart rate signals, very close to the ultrasound cardiotocographic recordings, considered as reference. The algorithm was also tested by using a foetal phonocardiographic recording simulator developed and presented in this research thesis. The target was to provide a software for simulating recordings relative to different foetal conditions and recordings situations and to use it as a test tool for comparing and assessing different foetal heart rate extraction algorithms. Since there are few studies about foetal heart sounds time characteristics and frequency content and the available literature is poor and not rigorous in this area, a data collection pilot study was also conducted with the purpose of specifically characterising both foetal and maternal heart sounds. Finally, in this thesis, the use of foetal phonocardiographic and electrocardiographic methodology and their combination, are presented in order to detect foetal heart rate and other functioning anomalies. The developed methodologies, suitable for longer-term assessment, were able to detect heart beat events correctly, such as first and second heart sounds and QRS waves. The detection of such events provides reliable measures of foetal heart rate, potentially information about measurement of the systolic time intervals and foetus circulatory impedance.