On representing signals using only timing information

It is well known that only a special class of bandpass signals, called real-zero (RZ) signals can be uniquely represented (up to a scale factor) by their zero crossings, i.e., the time instants at which the signals change their sign. However, it is possible to invertibly map arbitrary bandpass signals into RZ signals, thereby, implicitly represent the bandpass signal using the mapped RZ signal’s zero crossings. This mapping is known as real-zero conversion (RZC). In this paper a class of novel signal-adaptive RZC algorithms is proposed. Specifically, algorithms that are analogs of well-known adaptive filtering methods to convert an arbitrary bandpass signal into other signals, whose zero crossings contain sufficient information to represent the bandpass signal’s phase and envelope are presented. Since the proposed zero crossings are not those of the original signal, but only indirectly related to it, they are called hidden or covert zero crossings (CoZeCs). The CoZeCs-based representations are developed first for analytic signals, and then extended to real-valued signals. Finally, the proposed algorithms are used to represent synthetic signals and speech signals processed through an analysis filter bank, and it is shown that they can be reconstructed given the CoZeCs. This signal representation has potential in many speech applications

A Sensitivity and Array-Configuration Study for Measuring the Power Spectrum of 21cm Emission from Reionization

Telescopes aiming to measure 21cm emission from the Epoch of Reionization must toe a careful line, balancing the need for raw sensitivity against the stringent calibration requirements for removing bright foregrounds. It is unclear what the optimal design is for achieving both of these goals. Via a pedagogical derivation of an interferometer's response to the power spectrum of 21cm reionization fluctuations, we show that even under optimistic scenarios, first-generation arrays will yield low-SNR detections, and that different compact array configurations can substantially alter sensitivity. We explore the sensitivity gains of array configurations that yield high redundancy in the uv-plane -- configurations that have been largely ignored since the advent of self-calibration for high-dynamic-range imaging. We first introduce a mathematical framework to generate optimal minimum-redundancy configurations for imaging. We contrast the sensitivity of such configurations with high-redundancy configurations, finding that high-redundancy configurations can improve power-spectrum sensitivity by more than an order of magnitude. We explore how high-redundancy array configurations can be tuned to various angular scales, enabling array sensitivity to be directed away from regions of the uv-plane (such as the origin) where foregrounds are brighter and where instrumental systematics are more problematic. We demonstrate that a 132-antenna deployment of the Precision Array for Probing the Epoch of Reionization (PAPER) observing for 120 days in a high-redundancy configuration will, under ideal conditions, have the requisite sensitivity to detect the power spectrum of the 21cm signal from reionization at a 3\sigma level at k<0.25h Mpc^{-1} in a bin of \Delta ln k=1. We discuss the tradeoffs of low- versus high-redundancy configurations.Comment: 34 pages, 5 figures, 2 appendices. Version accepted to Ap

Efficient Acquisition and Denoising of Full-Range Event-Related Potentials Following Transient Stimulation of the Auditory Pathway

This body of work relates to recent advances in the field of human auditory event-related potentials (ERP), specifically the fast, deconvolution-based ERP acquisition as well as single-response based preprocessing, denoising and subsequent analysis methods. Its goal is the contribution of a cohesive set of methods facilitating the fast, reliable acquisition of the whole electrophysiological response generated by the auditory pathway from the brainstem to the cortex following transient acoustical stimulation. The present manuscript is divided into three sequential areas of investigation : First, the general feasibility of simultaneously acquiring auditory brainstem, middle-latency and late ERP single responses is demonstrated using recordings from 15 normal hearing subjects. Favourable acquisition parameters (i.e., sampling rate, bandpass filter settings and interstimulus intervals) are established, followed by signal analysis of the resulting ERP in terms of their dominant intrinsic scales to determine the properties of an optimal signal representation with maximally reduced sample count by means of nonlinear resampling on a logarithmic timebase. This way, a compression ratio of 16.59 is achieved. Time-scale analysis of the linear-time and logarithmic-time ERP single responses is employed to demonstrate that no important information is lost during compressive resampling, which is additionally supported by a comparative evaluation of the resulting average waveforms - here, all prominent waves remain visible, with their characteristic latencies and amplitudes remaining essentially unaffected by the resampling process. The linear-time and resampled logarithmic-time signal representations are comparatively investigated regarding their susceptibility to the types of physiological and technical noise frequently contaminating ERP recordings. While in principle there already exists a plethora of well-investigated approaches towards the denoising of ERP single-response representations to improve signal quality and/or reduce necessary aquisition times, the substantially altered noise characteristics of the obtained, resampled logarithmic-time single response representations as opposed to their linear-time equivalent necessitates a reevaluation of the available methods on this type of data. Additionally, two novel, efficient denoising algorithms based on transform coefficient manipulation in the sinogram domain and on an analytic, discrete wavelet filterbank are proposed and subjected to a comparative performance evaluation together with two established denoising methods. To facilitate a thorough comparison, the real-world ERP dataset obtained in the first part of this work is employed alongside synthetic data generated using a phenomenological ERP model evaluated at different signal-to-noise ratios (SNR), with individual gains in multiple outcome metrics being used to objectively assess algorithm performances. Results suggest the proposed denoising algorithms to substantially outperform the state-of-the-art methods in terms of the employed outcome metrics as well as their respective processing times. Furthermore, an efficient stimulus sequence optimization method for use with deconvolution-based ERP acquisition methods is introduced, which achieves consistent noise attenuation within a broad designated frequency range. A novel stimulus presentation paradigm for the fast, interleaved acquisition of auditory brainstem, middle-latency and late responses featuring alternating periods of optimized, high-rate deconvolution sequences and subsequent low-rate stimulation is proposed and investigated in 20 normal hearing subjects. Deconvolved sequence responses containing early and middle-latency ERP components are fused with subsequent late responses using a time-frequency resolved weighted averaging method based on cross-trial regularity, yielding a uniform SNR of the full-range auditory ERP across investigated timescales. Obtained average ERP waveforms exhibit morphologies consistent with both literature values and the reference recordings obtained in the first part of this manuscript, with all prominent waves being visible in the grand average waveforms. The novel stimulation approach cuts acquisition time by a factor of 3.4 while at the same time yielding a substantial gain in the SNR of obtained ERP data. Results suggest the proposed interleaved stimulus presentation and associated postprocessing methodology to be suitable for the fast, reliable extraction of full-range neural correlates of auditory processing in future studies.Diese Arbeit steht im Zusammenhang mit aktuellen Entwicklungen auf dem Gebiet der ereigniskorrelierten Potentiale (EKP) des humanen auditorischen Systems, insbesondere der schnellen, entfaltungsbasierten EKP-Aufzeichnung sowie einzelantwortbasierten Vorverarbeitungs-, Entrauschungs- und nachgelagerten Analysemethoden. Ziel ist die Bereitstellung eines vollständigen Methodensatzes, der eine schnelle, zuverlässige Erfassung der gesamten elektrophysiologischen Aktivität entlang der Hörbahn vom Hirnstamm bis zum Cortex ermöglicht, die als Folge transienter akustischer Stimulation auftritt. Das vorliegende Manuskript gliedert sich in drei aufeinander aufbauende Untersuchungsbereiche : Zunächst wird die generelle Machbarkeit der gleichzeitigen Aufzeichnung von Einzelantworten der auditorischen Hirnstammpotentiale zusammen mit mittelspäten und späten EKP anhand von Referenzmessungen an 15 normalhörenden Probanden demonstriert. Es werden hierzu geeignete Erfassungsparameter (Abtastrate, Bandpassfiltereinstellungen und Interstimulusintervalle) ermittelt, gefolgt von einer Signalanalyse der resultierenden EKP im Hinblick auf deren dominante intrinsische Skalen, um auf dieser Grundlage die Eigenschaften einer optimalen Signaldarstellung mit maximal reduzierter Anzahl an Abtastpunkten zu bestimmen, die durch nichtlineare Neuabtastung auf eine logarithmische Zeitbasis realisiert wird. Hierbei wird ein Kompressionsverhältnis von 16.59 erzielt. Zeit-Skalen-Analysen der uniform und logarithmisch abgetasteten EKP-Einzelantworten zeigen, dass bei der kompressiven Neuabtastung keine relevante Information verloren geht, was durch eine vergleichende Auswertung der resultierenden, gemittelten Wellenformen zusätzlich gestützt wird - alle prominenten Wellen bleiben sichtbar und sind hinsichtlich ihrer charakteristischen Latenzen und Amplituden von der Neuabtastung weitgehend unbeeinflusst. Die uniforme und logarithmische Signalrepräsentation werden hinsichtlich ihrer Anfälligkeit für die üblicherweise bei der EKP-Aufzeichnung auftretenden physiologischen und technischen Störquellen vergleichend untersucht. Obwohl bereits eine Fülle von gut etablierten Ansätzen für die Entrauschung von EKP-Einzelantwortdarstellungen zur Verbesserung der Signalqualität und/oder zur Reduktion der benötigten Erfassungszeiten existiert, erfordern die wesentlich veränderten Störeigenschaften der vorliegenden, logarithmisch abgetasteten Einzelantwortdarstellungen im Gegensatz zu ihrem uniformen Äquivalent eine Neubewertung der verfügbaren Methoden für diese Art von Daten. Darüber hinaus werden zwei neuartige, effiziente Entrauschungsalgorithmen geboten, die auf der Koeffizientenmanipulation einer Sinogramm-Repräsentation bzw. einer analytischen, diskreten Wavelet-Zerlegung der Einzelantworten basieren und gemeinsam mit zwei etablierten Entrauschungsmethoden einer vergleichenden Leistungsbewertung unterzogen werden. Um einen umfassenden Vergleich zu ermöglichen, werden der im ersten Teil dieser Arbeit erhaltene EKP-Messdatensatz sowie synthetischen Daten eingesetzt, die mithilfe eines phänomenologischen EKP-Modells bei verschiedenen Signal-Rausch-Abständen (SRA) erzeugt wurden, wobei die individuellen Anstiege in mehreren Zielmetriken zur objektiven Bewertung der Performanz herangezogen werden. Die erhaltenen Ergebnisse deuten darauf hin, dass die vorgeschlagenen Entrauschungsalgorithmen die etablierten Methoden sowohl in den eingesetzten Zielmetriken als auch mit Blick auf die Laufzeiten deutlich übertreffen. Weiterhin wird ein effizientes Reizsequenzoptimierungsverfahren für den Einsatz mit entfaltungsbasierten EKP-Aufzeichnungsmethoden vorgestellt, das eine konsistente Rauschunterdrückung innerhalb eines breiten Frequenzbands erreicht. Ein neuartiges Stimulus-Präsentationsparadigma für die schnelle, verschachtelte Erfassung auditorischer Hirnstammpotentiale, mittlelspäter und später Antworten durch alternierende Darbietung von optimierten, dichter Stimulussequenzen und nachgelagerter, langsamer Einzelstimulation wird eingeführt und in 20 normalhörenden Probanden evaluiert. Entfaltete Sequenzantworten, die frühe und mittlere EKP enthalten, werden mit den nachfolgenden späten Antworten fusioniert, wobei eine Zeit-Frequenz-aufgelöste, gewichtete Mittelung unter Berücksichtigung von Regularität über Einzelantworten hinweg zum Einsatz kommt. Diese erreicht einheitliche SRA der resultierenden EKP-Signale über alle untersuchten Zeitskalen hinweg. Die erhaltenen, gemittelten EKP-Wellenformen weisen Morphologien auf, die sowohl mit einschlägigen Literaturwerten als auch mit den im ersten Teil dieses Manuskripts erhaltenen Referenzaufnahmen konsistent sind, wobei alle markanten Wellen deutlich in den Gesamtmittelwerten sichtbar sind. Das neuartige Stimulationsparadigma verkürzt die Erfassungszeit um den Faktor 3.4 und vergrößert gleichzeitig den erreichten SRA erheblich. Die Ergebnisse deuten darauf hin, dass die vorgeschlagene verschachtelte Stimuluspräsentation und die nachgelagerte EKP-Verarbeitungsmethodik zur schnellen, zuverlässigen Extraktion neuronaler Korrelate der gesamten auditorischen Verarbeitung im Rahmen zukünftiger Studien geeignet sind.Bundesministerium für Bildung und Forschung | Bimodal Fusion - Eine neurotechnologische Optimierungsarchitektur für integrierte bimodale Hörsysteme | 2016-201

Optical Space Division Multiplexing in Short Reach Multi-Mode Fiber Systems

The application of space division multiplexing to fiber-optic communications is a promising approach to further increase the channel capacity of optical waveguides. In this work, short reach and low-cost optical space division multiplexing systems with intensity modulation and direct detection (IM/DD) are in the focus of interest. Herein, different modes are utilized to generate spatial diversity in a multi-mode fiber. In such IM/DD systems, the process of square-law detection is inherently non-linear. In order to obtain an understanding of the channel characteristics, a system model is developed, which is able to show under which conditions the system can be considered linear in baseband. It is shown that linearity applies in scenarios with low mode cross-talk. This enables the use of linear multiple-input multiple-output (MIMO) signal processing strategies for equalization purposes. In conditions with high mode cross-talk, significant interference occurs, and the transmitted information cannot be extracted at the receiver. Furthermore, a method to determine the power coupling coefficients between mode groups is presented that does not require the excitation of individual modes, and hence it can be realized with inexpensive components. In addition, different optical components are analyzed with respect for their suitability in MIMO setups with IM/DD. The conventional approach with single-mode fiber to multi-mode fiber offset launches and optical couplers as well as a configuration that utilizes multi-segment detection are feasible options for a (2x2) setup. It is further shown that conventional photonic lanterns are not suited for MIMO with IM/DD due to their low mode orthogonality during the multiplexing process. In order to enable higher order MIMO configurations, devices for mode multiplexing and demultiplexing need to be developed, which exhibit a high mode orthogonality on one hand and are low-cost on the other hand

Investigating Economic Trends And Cycles

Methods are described for extracting the trend from an economic data sequence and for isolating the cycles that surround it. The latter often consist of a business cycle of variable duration and a perennial seasonal cycle. There is no evident point in the frequency spectrum where the trend ends and the business cycle begins. Therefore, unless it can be represented by a simple analytic function, such as an exponential growth path, there is bound to be a degree of arbitrariness in the definition of the trend. The business cycle, however defined, is liable to have an upper limit to its frequency range that falls short of the Nyquist frequency, which is the maximum observable frequency in sampled data. This must be taken into account in fitting an ARMA model to the detrended data.

The role of zero crossings in speech recognition and processing

Imperial Users onl

IF-level signal-processing of GPS and Galileo Radionavigation signals using MATLAB/Simulink®: Including Effects of Interference and Multipath

Open-source GNSS simulator models are rare and somewhat difficult to find. Therefore, Laboratory of Electronics and Communications Engineering in the former Tampere University of Technology (and now Tampere University, Hervanta Campus) has took it upon itself to develop, from time to time, a free and open-source simulator model based on MATLAB/Simulink® for signal processing of a carefully selected set of GNSS radionavigation signals, namely, Galileo E1, Galileo E5, GPS L1, and GPS L5. This M.Sc. thesis is the culmination of those years which have been spent intermittently on research and development of that simulator model. The first half of this M.Sc. thesis is a literature review of some topics which are believed to be of relevance to the thesis’s second half which is in turn more closely associated with documenting the simulator model in question. In particular, the literature review part presents the reader with a plethora of GNSS topics ranging from history of GNSS technology to characteristics of existing radionavigation signals and, last but not least, compatibility and interoperability issues among existing GNSS constellations. While referring to the GNSS theory whenever necessary, the second half is, however, mainly focused on describing the inner-workings of the simulator model from the standpoint of software implementations. Finally, the second half, and thereby the thesis, is concluded with a presentation of various statistical results concerning signal acquisition’s probabilities of detection and false-alarm, in addition to signal tracking’s RMSE

SETI science working group report

This report covers the initial activities and deliberations of a continuing working group asked to assist the SETI Program Office at NASA. Seven chapters present the group's consensus on objectives, strategies, and plans for instrumental R&D and for a microwave search for extraterrestrial in intelligence (SETI) projected for the end of this decade. Thirteen appendixes reflect the views of their individual authors. Included are discussions of the 8-million-channel spectrum analyzer architecture and the proof-of-concept device under development; signal detection, recognition, and identification on-line in the presence of noise and radio interference; the 1-10 GHz sky survey and the 1-3 GHz targeted search envisaged; and the mutual interests of SETI and radio astronomy. The report ends with a selective, annotated SETI reading list of pro and contra SETI publications

Adaptive Estimation and Compensation of the Time Delay in a Periodic Non-uniform Sampling Scheme

High sampling rate Analog-to-Digital Converters (ADCs) can be obtained by time-interleaving low rate (and thus low cost) ADCs into so-called Time-Interleaved ADCs (TI-ADCs). Nevertheless increasing the sampling frequency involves an increasing sensibility of the system to desynchronization between the different ADCs that leads to time-skew errors, impacting the system with non linear distortions. The estimation and compensation of these errors are considered as one of the main challenge to deal with in TI-ADCs. Some methods have been previously proposed, mainly in the field of circuits and systems, to estimate the time-skew error but they mainly involve hardware correction and they lack of flexibility, using an inflexible uniform sampling reference. In this paper, we propose to model the output of L interleaved and desynchronized ADCs with a sampling scheme called Periodic Non-uniform Sampling of order L (PNSL). This scheme has been initially proposed as an alternative to uniform sampling for aliasing cancellation, particularly in the case of bandpass signals. We use its properties here to develop a flexible on-line digital estimation and compensation method of the time delays between the desynchronized channels. The estimated delay is exploited in the PNSL reconstruction formula leading to an accurate reconstruction without hardware correction and without any need to adapt the sampling operation. Our method can be used in a simple Built-In Self-Test (BIST) strategy with the use of learning sequences and our model appears more flexible and less electronically expensive, following the principles of “Dirty Radio Frequency” paradigm: designing imperfect analog circuits with subsequently digital corrections of these imperfections