We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. We present a generalization of the BO equation called the non-chiral Intermediate wave (ncILW) equation and show that a family of solutions to the ncILW equation can be constructed from the special Lax function corresponding to the hyperbolic CMS system. We present the Szegö equation on the circle and the real line. We obtain a family of solutions to the Szegö equation on the real line using a pole ansatz. Using numerical methods, we display solution plots to the BO equation and Szegö equation.

This thesis deals with generalizations of the analytic signal (AS) construction proposed by Gabor. Functional extensions of the fractional Hilbert Transform (FrHT) are proposed using which families of analytic signals are obtained. The construction is further applied in the design of a secure communication scheme. A demodulation scheme is developed based on the generalized AS, motivated by perceptual experiments in binaural hearing. Demodulation is achieved using a signal and its arbitrary phase-shifted version which, in turn translated to demodulation using a pair of flat-top bandpass filters that form an FrHT parir. A new family of wavelets based on the popular Gammatone auditory model is proposed and is shown to lead to a good characterization of singularities/transients in a signal. Allied problems of computing smooth amplitude, phase, and frequency modulations from the AS. Construction of FrHT pair of wavelets, and temporal envelope fit of transient audio signals are also addressed.

No description available.

Cognitive radios require spectral occupancy information in a given location, to avoid any interference with the existing licensed users. This is achieved by spectrum sensing. Existing narrowband, serial spectrum sensors are spectrally inefficient and power hungry. Wideband spectrum sensing increases the number of probable fre-quency candidates for cognitive radio. Wideband RF systems cannot use analog to digital converters (ADCs) for spectrum sensing without increasing the sampling rate and power consumption. The use of ADCs is limited because of the dynamic range of the signals that need to be sampled and the frequency of operation. In this work, we have presented a CMOS based area efficient, dedicated and scalable wideband parallel/serial spectrum sensor for cognitive radio. The key contributions of the thesis are: 1. An injection locked oscillator cascade (ILOC) for parallel LO synthesis. An area-efficient, wideband RF frequency synthesizer, which simultaneously gen-erates multiple local oscillator (LO) signals, is designed. It is suitable for parallel wideband RF spectrum sensing in cognitive radios. The frequency synthesizer consists of an injection locked oscillator cascade where all the LO signals are derived from a single reference oscillator. The ILOC is implemented in a 130-nm technology with an active area of 0.017 mm2. It generates 4 uni-formly spaced LO carrier frequencies from 500 MHz to 2 GHz. 2. A wideband, parallel RF spectrum sensor for cognitive radios has been de-signed. This spectrum sensor is designed to detect RF occupancy from 250 MHz to 5.25 GHz by using an array of CMOS receivers with envelope detec-tors. A parallel LO synthesizer is implemented as an ILOC. The simulated sensitivity is around -25 dBm for 250 MHz wide bandwidth. 3. A mitigation technique for harmonic downconversion in wideband spectrum sensors. The downconversion of radio frequency (RF) components around the harmonics of the local oscillator (LO), and its impact on the accuracy of white space detection using integrated spectrum sensors, is (are) studied. We propose an algorithm to mitigate the impact of harmonic Down conversion by utilizing multiple parallel downconverters in the system architecture. The proposed algorithm is validated on a test-board using commercially avail-able integrated circuits (IC) and a test-chip implemented in a 130-nm CMOS technology. The measured data shows that the impact of the harmonic down-conversion is closely related to the LO characteristics, and that much of it can be mitigated by the proposed technique. 4. A wideband spectrum sensor for narrowband energy detection. A wideband spectrum sensing system for cognitive radio is designed and implemented in a 130-nm RF mixed-mode CMOS technology. The system employs an I-Q downconverter, a pair of complex filters and a pair of envelope detectors for energy detection. The spectrum sensor works from 250 MHz to 3.25 GHz. The design makes use of the band pass nature of the complex filter to achieve two objectives : i) Separation of upper sideband (USB) and lower sideband (LSB) around the local oscillator (LO) signal and ii) Resolution of smaller bands within a large detection bandwidth. The measured sensitivity is close to -45 dBm for a single tone test over a bandwidth of 40 MHz. The measured Image reject ratio (IRR) is close to 30 dB. The overall sensing bandwidth is 3.5 GHz and the overall wideband detection bandwidth is 250 MHz which is partitioned into 40 MHz narrowband chunks with 8 such overlapping chunks.

The aim of the master’s thesis is to acquaint the reader with Discrete Fourier Transform DFT and its introduction to spectral analysis descrete time signals. Furthermore it describes efficient computation of the DFT using the algorithm Fast Fourier Transform FFT and effects that appear in the DFT spectral analysis, the effect of the length of the DFT, the effect of the length of the segment of the analysed signal and the leakage. Next is explained the issue of the complex representation of real bandpass signals in the baseband, called the complex envelope of signals. This represenation uses the Hilbert Transform and the analytic signal. The thesis also describes the application library Real Time Toolbox of the software Matlab/Simulink, that uses the data acquition card AD622 allows to connect and process real signals in real time. In Matlab/Simulink with use this facilities is create the laboratory lesson, that simulating the complex represenation of real bandpass signals in real time.

This paper discusses the possible use of Hilbert-Huang transform to analyze the data obtained from physical experiments. Specifically for the analysis of acoustic emission in the form of acoustic shock. The introductory section explains the concept of acoustic emission and its detection process. Subsequently are discussed methods for signal analysis in time-frequency domain. Specifically, short-term Fourier transform, Wavelet transform, Hilbert transform and Hilbert-Huang transform. The final part contains the proposed method for measuring the performance and accuracy of different approaches.

The thesis is focused on the study of detection of QRS complex in time a frequency domain. The aim is to implement selected methods and their comparison to assess the effectiveness of QRS complex.

The present final thesis discusses the transmission of a narrowly directional parametric sound beam through an amplitude-modulated ultrasonic wave, utilizing the effect of auto-demodulation in a nonlinear medium and ensuring the subsequent processing of the input signal for the parametric sound transmitter. Emphasis is placed on the mathematical tools that relate to parametric sound transmission in a nonlinear medium. The basic part of the thesis describes a parametric speaker and the associated amplitude modulation techniques, which constitute a major prerequisite for the processing of the transmitted signal. In the following section, the author then analyzes the computational intensity of these techniques, considering applicable hardware approaches. Finally, the fabrication and practical use of the proposed solution are discussed, including the measurement of typical parameters such as the spatial radiation characteristics, total harmonic distortion, and transmission channel bandwidth.

This dissertation thesis deals with the methods for processing image data in X-ray microtomography and digital holographic microscopy. The work aims to achieve significant acceleration of algorithms for tomographic reconstruction and image reconstruction in holographic microscopy by means of optimization and the use of massively parallel GPU. In the field of microtomography, the new GPU (graphic processing unit) accelerated implementations of filtered back projection and back projection filtration of derived data are presented. Another presented algorithm is the orientation normalization technique and evaluation of 3D tomographic data. In the part related to holographic microscopy, the individual steps of the complete image processing procedure are described. This part introduces the new orignal technique of phase unwrapping and correction of image phase damaged by the occurrence of optical vortices in the wrapped image phase. The implementation of the methods for the compensation of the phase deformation and for tracking of cells is then described. In conclusion, there is briefly introduced the Q-PHASE software, which is the complete bundle of all the algorithms necessary for the holographic microscope control, and holographic image processing.

While signatures of attention can be observed in widespread areas within and outside of cortex, the control of attention is thought to be regulated by higher cognitive brain areas, such as the prefrontal cortex. In their recent study on mice Kim et al. could show that successful allocation of attention is characterized by increased spiking of a specific type of inhibitory interneurons, the parvalbumin neurons, and higher oscillatory activity in the gamma band in the local prefrontal network. It was recently demonstrated that encoding of working memory in prefrontal areas is linked to bursts of gamma oscillations, a discontinuous network process characterized by short periods of intense power in the gamma band. The relationship between attention and working memory is unclear, and it is possible that these two cognitive processes share encoding principles. To address this gap, the electrophysiological data collected in the Carlén Lab have been analyzed with advanced spatio-temporal approaches. In particular, we have analyzed bursting gamma activity in medial prefrontal cortex during attentional processing and investigated the similarities to gamma bursting observed during working memory. Gamma-band bursts during attention were reliably detected with several methods. We have characterized several features of the bursts, including the occurrence, duration and amplitude. The neuronal firing rates during and outside of bursts have also been computed. We investigated the correlation between different criteria characterizing the gamma burst and successful vs failed allocation of attention. Control data were generated to discuss the obtained results. The aim of the study was to explore the hypothesis that the medial prefrontal cortex encodes attention trough gamma bursts, which could reveal some similarities and differences in coding of central cognitive processes. No clear difference was found in the characterization between successful and failed allocation of attention. In addition, results were very similar in control set and original data. No underlying mechanism could be identified from this analysis. Therefore, as the bursts occurring in the gamma band in the prefrontal cortex (PFC) were not discriminative with respect to the different tested conditions, they do not seem to encode information related to attention. / Även fast flera olika hjärnområdens aktivitet kan korreleras med uppmärksamhet, anses kontrollen av uppmärksamhet regleras av högre kognitiva hjärnområden, såsom främre hjärnbarken. I en nyligen publicerad artikel studerade Kim et al. hjärnaktiviteten hos möss och kunde visa att en framgångsrik uppmärksamhet kännetecknas av en ökad aktivitet av en specifik typ av inhiberande nervceller, parvalbumin celler, och högre oscillerande aktivitet i gammafrekvens i främre hjärnbarkens lokala nätverk. Det har nyligen visats att kodning av arbetsminne i främre hjärnbarken är kopplat till utbrott av gamma-oscillationer, en diskontinuerlig nätverksprocess som kännetecknas av korta perioder av intensiva oscillationer av det lokala nätverket i gammafrekvens . Relationen mellan uppmärksamhet och arbetsminne är oklar, och det är möjligt att dessa två kognitiva processer delar kodningsprinciper. För att minska detta gap av kunskap har den elektrofysiologiska datan som samlats in i Carlén Lab analyserats med avancerade spatio-temporala tillvägagångssätt. I synnerhet har vi analyserat utbrott i gammaaktivitet i främre hjärnbarken under uppmärksamhet och undersökt likheterna med gamma- utbrott observerade under arbetsminne. Gamma-bandutbrott under uppmärksamhet påvisades på ett tillförlitligt sätt med flera metoder. Vi har karaktäriserat flera funktioner hos utbrotten, inklusive förekomsten, varaktigheten och amplituden. De enskilda cellernas aktivitet undersöktes även under och utanför utprotten av gamma-oscillationer. Vi undersökte sambandet mellan de olika kriterier som karakteriserar gamma-utbrott under framgångsrik mot misslyckad allokering av uppmärksamhet. Kontrolldata genererades för att diskutera de erhållna resultaten. Syftet med studien var att utforska hypotesen att den främre hjärnbarken kodar uppmärksamhet genom gamma-utbrott, vilket kan avslöja vissa likheter och skillnader i kodning av centrala kognitiva processer. Ingen klar skillnad hittades i karaktäriseringen mellan framgångsrik och misslyckad allokering av uppmärksamhet. Dessutom var resultaten mycket likartade i kontrolluppsättningen och den ursprungliga datan. Ingen underliggande mekanism kunde identifieras ur denna analys. Eftersom de utbrott som uppstod i gamma-bandet i främre hjärnbarken inte var unika med hänsyn till de olika testade förhållandena, tycks de därför inte koda information relaterad till uppmärksamhet.