Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.

京都大学 / 新制・論文博士 / 博士(医学) / 乙第13513号 / 論医博第2263号 / 新制||医||1061(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 伊佐 正, 教授 村井 俊哉, 教授 高橋 淳 / 学位規則第4条第2項該当 / Doctor of Medical Science / Kyoto University / DFAM

No / This paper presents a novel and hardware-efficient architecture for power-of-two FFT processors. The proposed design is based on the phase-amplitude splitting technique which converts a DFT to cyclic convolutions and additions. The cyclic convolutions are implemented with a filter-like structure and the additions are computed with several stages of butterfly processing units. The proposed architecture requires no multiplier, and comparisons with other designs show it can save up to 39% total equivalent gates for an 8-bit 16-point FPGA-based FFT processor.

<p>Detta examensarbete utröner möjligheten att aktivt släcka ut en amplitudstark frekvensmodulerad sinussignal digitalt. Detta skall göras utan förkunskap om signalen gällande fas, frekvens eller amplitud. Eventuellt övriga, men betydligt svagare, sinussignaler i den analoga signalen skall inte påverkas nämnvärt av utsläckningen. För att lösa problemet har olika teorier för att lösa delproblemen med att mäta amplitud, fas och frekvens studerats varefter en lämplig kombination valts för implementering i en FPGA. Prestandan som uppmätts har jämförts med vad som teoretiskt är möjligt och vi konstaterar att metoden löser problemet på ett adekvat sätt men är i behov av en del förbättringar som diskuteras i slutet.</p> / <p>This master thesis investigates the possibility to cancel a frequency modulated sinusoid with high amplitude in the digital domain. This will be done without any pre-knowledge of the signal regarding phase, frequency or amplitude. Other arbitrary, but weaker, sinusoids present in the analog signal should not be noticeable affected by the cancellation. To solve the partial problems of measuring amplitude, frequency and phase, different theories have been studied and thereafter a suitable combination was chosen for implementation in a Field Programmable Gate Array, FPGA. The performance measured has been compared to the theoretical maximum performance and it has been concluded that the proposed implementation solves this problem adequately but needs some enhancements, these are discussed in the final chapter.</p>

Detta examensarbete utröner möjligheten att aktivt släcka ut en amplitudstark frekvensmodulerad sinussignal digitalt. Detta skall göras utan förkunskap om signalen gällande fas, frekvens eller amplitud. Eventuellt övriga, men betydligt svagare, sinussignaler i den analoga signalen skall inte påverkas nämnvärt av utsläckningen. För att lösa problemet har olika teorier för att lösa delproblemen med att mäta amplitud, fas och frekvens studerats varefter en lämplig kombination valts för implementering i en FPGA. Prestandan som uppmätts har jämförts med vad som teoretiskt är möjligt och vi konstaterar att metoden löser problemet på ett adekvat sätt men är i behov av en del förbättringar som diskuteras i slutet. / This master thesis investigates the possibility to cancel a frequency modulated sinusoid with high amplitude in the digital domain. This will be done without any pre-knowledge of the signal regarding phase, frequency or amplitude. Other arbitrary, but weaker, sinusoids present in the analog signal should not be noticeable affected by the cancellation. To solve the partial problems of measuring amplitude, frequency and phase, different theories have been studied and thereafter a suitable combination was chosen for implementation in a Field Programmable Gate Array, FPGA. The performance measured has been compared to the theoretical maximum performance and it has been concluded that the proposed implementation solves this problem adequately but needs some enhancements, these are discussed in the final chapter.

Antenna is an indispensable part of a radar or free space communication system. Antenna requires different stringent specifications for different applications. Designed and fabricated for an intended application, antenna or antenna array has to be evaluated for its far-field characteristics in real free space environment which requires setting up of far-field test site. Maintenance of the site to keep the stray reflections levels low, the cost of the real estate are some of the disadvantages. Nearfield measurements are compact and can be used to test the antennas by exploiting the relationship between near-field and far-field. It is shown that the far-field patterns of an antenna can be sufficiently accurately predicted provided the near-field measurements are accurate. Due to limitation in the near-field measurement systems, errors creep in corrupting the nearfield-measured data thus making error in prediction of the far field. All these errors ultimately corrupt the phase and amplitude data. In this thesis, one such near-field measurement facility, the Planar Near Field Measurement facility is discussed. The limitations of the facility and the errors that occur due to their limitations are discussed. Various errors that occur in measurements ultimately corrupt the near-field phase and amplitude. Investigations carried out aim at a detailed study of these phase and amplitude errors and their effect on the far-field patterns of the antenna. Depending on the source of error, the errors are classified as spike, pulse and random errors. The location of occurrence of these types of errors in the measurement plane, their effects on the far-field of the antenna is studied both for phase and amplitude errors. The studies conducted for various phase and amplitude errors show that the near-field phase and amplitude data are more tolerant to random errors as the far-field patterns do not get affected even for low sidelobe cases. The spike errors, though occur as a wedge at a single point in the measurement plane, have more pronounced effect on the far-field patterns. Lower the taper value of the antenna, more pronounced is the error. It is also noticed that the far-field pattern gets affected only in the plane where the error has occurred and has no effect in the orthogonal plane. Pulse type of errors which occur even for a short length in the measurement affect both the principle plane far-field patterns. This study can be used extensively as a tool to determine to the level to which various error such as mechanical, RF etc need to be controlled to make useful and correct pattern predictions on a particular facility. Thereby, the study can be used as a tool to economise the budget of the facility wherein the parameters required for building the facility need not be over specified beyond the requirement. In general, though this is a limited study, it is certainly a trendsetter in this direction.

Le futur système de transmission multicanaux (WDM) pourrait mettre à profit l'utilisation d'amplificateurs optiques à semi-conducteurs (SOA), pour bénéficier notamment de leur grande bande passante optique pour l'amplification du signal. Dans ce travail, nous étudions l’influence des SOA sur la transmission cohérente de signaux OFDM optiques (CO OFDM). Cette technique, récemment proposée, permet à la fois d’augmenter l'efficacité spectrale de la transmission et de compenser les imperfections linéaires du canal optique. Nous avons développé, dans ce travail, une chaîne expérimentale de transmission de signaux à formats de modulation complexes tout-optiques et une plateforme de simulation au niveau système. Les résultats obtenus par simulation, au niveau composant et au niveau système, sont en très bon accord avec ceux obtenus par les mesures expérimentales à la fois pour des formats de modulation QPSK et QPSK CO-OFDM. À travers différentes mesures et simulations, l’étude a permis de cerner clairement l’influence des paramètres du SOA sur la qualité de transmission des données. Les non-linéarités induites par le SOA, telles que le couplage phase amplitude, l’auto modulation du gain et de la phase (SGM et SPM), la modulation croisée du gain et de la phase (XGM et XPM) et le mélange à quatre ondes (FWM), jouent de façon importante sur les performances de ce format de modulation multi-porteuses ; leur influence a donc été analysée avec précision. Les connaissances acquises permettront à l’avenir d’une part de mieux définir les conditions d’utilisation des SOA dans les réseaux de transmission et d’autre part aideront à l’optimisation de nouvelles structures de SOA conçues pour la transmission de données à très haut débit utilisant des formats de modulation complexes. / Future wavelength division multiplexing (WDM) systems might take advantage from the use of semiconductor optical amplifiers (SOA), especially to benefit from their large optical bandwidth for signal amplification. In this work, we study the influence of SOAs on the coherent optical-OFDM (CO OFDM) transmission system. This recently proposed technique allows both to increase the spectral efficiency of the transmission and to compensate the linear imperfections of the optical channel. In this work, we have developed an experimental setup for signal transmission operating with advanced optical modulation formats and a system level simulation platform. Simulation results, both at the component level and at the system level, are in very good agreement with those obtained from experimental measurements in the case of both QPSK and QPSK CO-OFDM signals. The study has clearly identified, through various measurements and simulations, the influence of SOA parameters on the quality of data transmission. Nonlinearities induced by the SOA, such as phase-amplitude coupling, self gain and phase modulation (SGM and SPM), cross gain and phase modulation (XGM and XPM) and the four-wave mixing (FWM) affect the performances of this multicarrier modulation format. Their influence is studied very precisely in this work. This acquired knowledge will allow, on the one hand, better defining the conditions of use of SOAs in the transmission networks and, on the other hand, helping to optimize new structures of SOA designed for very high bit rate data transmissions using complex modulation formats.

Le futur système de transmission multicanaux (WDM) pourrait mettre à profit l'utilisation d'amplificateurs optiques à semi-conducteurs (SOA), pour bénéficier notamment de leur grande bande passante optique pour l'amplification du signal. Dans ce travail, nous étudions l'influence des SOA sur la transmission cohérente de signaux OFDM optiques (CO OFDM). Cette technique, récemment proposée, permet à la fois d'augmenter l'efficacité spectrale de la transmission et de compenser les imperfections linéaires du canal optique. Nous avons développé, dans ce travail, une chaîne expérimentale de transmission de signaux à formats de modulation complexes tout-optiques et une plateforme de simulation au niveau système. Les résultats obtenus par simulation, au niveau composant et au niveau système, sont en très bon accord avec ceux obtenus par les mesures expérimentales à la fois pour des formats de modulation QPSK et QPSK CO-OFDM. À travers différentes mesures et simulations, l'étude a permis de cerner clairement l'influence des paramètres du SOA sur la qualité de transmission des données. Les non-linéarités induites par le SOA, telles que le couplage phase amplitude, l'auto modulation du gain et de la phase (SGM et SPM), la modulation croisée du gain et de la phase (XGM et XPM) et le mélange à quatre ondes (FWM), jouent de façon importante sur les performances de ce format de modulation multi-porteuses ; leur influence a donc été analysée avec précision. Les connaissances acquises permettront à l'avenir d'une part de mieux définir les conditions d'utilisation des SOA dans les réseaux de transmission et d'autre part aideront à l'optimisation de nouvelles structures de SOA conçues pour la transmission de données à très haut débit utilisant des formats de modulation complexes.