From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin

End-to-end simulations of different coronagraphic techniques

The NASA exoplanet exploration program is dedicated to developing technologies for detecting and characterizing extrasolar planets. In support of that program we have evaluated three different coronagraphic techniques (bandlimited Lyot, optical vortex, and phase-induced pupil apodization) using optical propagation simulations. These utilized a complete hypothetical telescope+coronagraph system with phase and amplitude aberrations. Wavefront control using dual sequential deformable mirrors was performed. We discuss the different computational techniques necessary to accurately simulate each coronagraph

Perceptual Model-Driven Authoring of Plausible Vibrations from User Expectations for Virtual Environments

One of the central goals of design is the creation of experiences that are rated favorably in the intended application context. User expectations play an integral role in tactile product quality and tactile plausibility judgments alike. In the vibrotactile authoring process for virtual environments, vibra-tion is created to match the user’s expectations of the presented situational context. Currently, inefficient trial and error approaches attempt to match expectations implicitly. A more efficient, model-driven procedure based explicitly on tactile user expectations would thus be beneficial for author-ing vibrations. In everyday life, we are frequently exposed to various whole-body vibrations. Depending on their temporal and spectral proper-ties we intuitively associate specific perceptual properties such as “tin-gling”. This suggests a systematic relationship between physical parame-ters and perceptual properties. To communicate with potential users about such elicited or expected tactile properties, a standardized design language is proposed. It contains a set of sensory tactile perceptual attributes, which are sufficient to characterize the perceptual space of vibration encountered in everyday life. This design language enables the assessment of quantita-tive tactile perceptual specifications by laypersons that are elicited in situational contexts such as auditory-visual-tactile vehicle scenes. Howev-er, such specifications can also be assessed by providing only verbal de-scriptions of the content of these scenes. Quasi identical ratings observed for both presentation modes suggest that tactile user expectations can be quantified even before any vibration is presented. Such expected perceptu-al specifications are the prerequisite for a subsequent translation into phys-ical vibration parameters. Plausibility can be understood as a similarity judgment between elicited features and expected features. Thus, plausible vibration can be synthesized by maximizing the similarity of the elicited perceptual properties to the expected perceptual properties. Based on the observed relationships between vibration parameters and sensory tactile perceptual attributes, a 1-nearest-neighbor model and a regression model were built. The plausibility of the vibrations synthesized by these models in the context of virtual auditory-visual-tactile vehicle scenes was validat-ed in a perceptual study. The results demonstrated that the perceptual spec-ifications obtained with the design language are sufficient to synthesize vibrations, which are perceived as equally plausible as recorded vibrations in a given situational context. Overall, the demonstrated design method can be a new, more efficient tool for designers authoring vibrations for virtual environments or creating tactile feedback. The method enables further automation of the design process and thus potential time and cost reductions.:Preface III Abstract V Zusammenfassung VII List of Abbreviations XV 1 Introduction 1 1.1 General Introduction 1 1.1 Objectives of the Thesis 4 1.2 Structure of the Thesis 4 2. Tactile Perception in Real and Virtual Environments 7 2.1 Tactile Perception as a Multilayered Process 7 2.1.1 Physical Layer 8 2.1.2 Mechanoreceptor Layer 9 2.1.3 Sensory Layer 19 2.1.4 Affective Layer 26 2.2 Perception of Virtual Environments 29 2.2.1 The Place Illusion 29 2.2.2 The Plausibility Illusion 31 2.3 Approaches for the Authoring of Vibrations 38 2.3.1 Approaches on the Physical Layer 38 2.3.2 Approaches on the Mechanoreceptor Layer 40 2.3.3 Approaches on the Sensory Layer 40 2.3.4 Approaches on the Affective Layer 43 2.4 Summary 43 3. Research Concept 47 3.1 Research Questions 47 3.1.1 Foundations of the Research Concept 47 3.1.2 Research Concept 49 3.2 Limitations 50 4. Development of the Experimental Setup 53 4.1 Hardware 53 4.1.1 Optical Reproduction System 53 4.1.2 Acoustical Reproduction System 54 4.1.3 Whole-Body Vibration Reproduction System 56 4.2 Software 64 4.2.1 Combination of Reproduction Systems for Unimodal and Multimodal Presentation 64 4.2.2 Conducting Perceptual Studies 65 5. Assessment of a Sensory Tactile Design Language for Characterizing Vibration 67 5.1.1 Design Language Requirements 67 5.1.2 Method to Assess the Design Language 69 5.1.3 Goals of this Chapter 70 5.2 Tactile Stimuli 72 5.2.1 Generalization into Excitation Patterns 72 5.2.2 Definition of Parameter Values of the Excitation Patterns 75 5.2.3 Generation of the Stimuli 85 5.2.4 Summary 86 5.3 Assessment of the most relevant Sensory Tactile Perceptual Attributes 86 5.3.1 Experimental Design 87 5.3.2 Participants 88 5.3.3 Results 88 5.3.4 Aggregation and Prioritization 89 5.3.5 Summary 91 5.4 Identification of the Attributes forming the Design Language 92 5.4.1 Experimental Design 93 5.4.2 Participants 95 5.4.3 Results 95 5.4.4 Selecting the Elements of the Sensory Tactile Design Language 106 5.4.5 Summary 109 5.5 Summary and Discussion 109 5.5.1 Summary 109 5.5.2 Discussion 111 6. Quantification of Expected Properties with the Sensory Tactile Design Language 115 6.1 Multimodal Stimuli 116 6.1.1 Selection of the Scenes 116 6.1.2 Recording of the Scenes 117 6.1.3 Recorded Stimuli 119 6.2 Qualitative Communication in the Presence of Vibration 123 6.2.1 Experimental Design 123 6.2.2 Participants 124 6.2.3 Results 124 6.2.4 Summary 126 6.3 Quantitative Communication in the Presence of Vibration 126 6.3.1 Experimental Design 127 6.3.2 Participants 127 6.3.3 Results 127 6.3.4 Summary 129 6.4 Quantitative Communication in the Absence of Vibration 129 6.4.1 Experimental Design 130 6.4.2 Participants 132 6.4.3 Results 132 6.4.4 Summary 134 6.5 Summary and Discussion 135 7. Synthesis Models for the Translation of Sensory Tactile Properties into Vibration 137 7.1 Formalization of the Tactile Plausibility Illusion for Models 139 7.1.1 Formalization of Plausibility 139 7.1.2 Model Boundaries 143 7.2 Investigation of the Influence of Vibration Level on Attribute Ratings 144 7.2.1 Stimuli 145 7.2.2 Experimental Design 145 7.2.3 Participants 146 7.2.4 Results 146 7.2.5 Summary 148 7.3 Comparison of Modulated Vibration to Successive Impulse-like Vibration 148 7.3.1 Stimuli 149 7.3.2 Experimental Design 151 7.3.3 Participants 151 7.3.4 Results 151 7.3.5 Summary 153 7.4 Synthesis Based on the Discrete Estimates of a k-Nearest-Neighbor Classifier 153 7.4.1 Definition of the K-Nearest-Neighbor Classifier 154 7.4.2 Analysis Model 155 7.4.3 Synthesis Model 156 7.4.4 Interpolation of acceleration level for the vibration attribute profile pairs 158 7.4.5 Implementation of the Synthesis 159 7.4.6 Advantages and Disadvantages 164 7.5 Synthesis Based on the Quasi-Continuous Estimates of Regression Models 166 7.5.1 Overall Model Structure 168 7.5.2 Classification of the Excitation Pattern with a Support Vector Machine 171 7.5.3 General Approach to the Regression Models of each Excitation Pattern 178 7.5.4 Synthesis for the Impulse-like Excitation Pattern 181 7.5.5 Synthesis for the Bandlimited White Gaussian Noise Excitation Pattern 187 7.5.6 Synthesis for the Amplitude Modulated Sinusoidal Excitation Pattern 193 7.5.7 Synthesis for the Sinusoidal Excitation Pattern 199 7.5.8 Implementation of the Synthesis 205 7.5.9 Advantages and Disadvantages of the Approach 208 7.6 Validation of the Synthesis Models 210 7.6.1 Stimuli 212 7.6.2 Experimental Design 212 7.6.3 Participants 214 7.6.4 Results 214 7.6.5 Summary 219 7.7 Summary and Discussion 219 7.7.1 Summary 219 7.7.2 Discussion 222 8. General Discussion and Outlook 227 Acknowledgment 237 References 237Eines der zentralen Ziele des Designs von Produkten oder virtuellen Um-gebungen ist die Schaffung von Erfahrungen, die im beabsichtigten An-wendungskontext die Erwartungen der Benutzer erfüllen. Gegenwärtig versucht man im vibrotaktilen Authoring-Prozess mit ineffizienten Trial-and-Error-Verfahren, die Erwartungen an den dargestellten, virtuellen Situationskontext implizit zu erfüllen. Ein effizienteres, modellgetriebenes Verfahren, das explizit auf den taktilen Benutzererwartungen basiert, wäre daher von Vorteil. Im Alltag sind wir häufig verschiedenen Ganzkörper-schwingungen ausgesetzt. Abhängig von ihren zeitlichen und spektralen Eigenschaften assoziieren wir intuitiv bestimmte Wahrnehmungsmerkmale wie z.B. “kribbeln”. Dies legt eine systematische Beziehung zwischen physikalischen Parametern und Wahrnehmungsmerkmalen nahe. Um mit potentiellen Nutzern über hervorgerufene oder erwartete taktile Eigen-schaften zu kommunizieren, wird eine standardisierte Designsprache vor-geschlagen. Sie enthält eine Menge von sensorisch-taktilen Wahrneh-mungsmerkmalen, die hinreichend den Wahrnehmungsraum der im Alltag auftretenden Vibrationen charakterisieren. Diese Entwurfssprache ermög-licht die quantitative Beurteilung taktiler Wahrnehmungsmerkmale, die in Situationskontexten wie z.B. auditiv-visuell-taktilen Fahrzeugszenen her-vorgerufen werden. Solche Wahrnehmungsspezifikationen können jedoch auch bewertet werden, indem der Inhalt dieser Szenen verbal beschrieben wird. Quasi identische Bewertungen für beide Präsentationsmodi deuten darauf hin, dass die taktilen Benutzererwartungen quantifiziert werden können, noch bevor eine Vibration präsentiert wird. Die erwarteten Wahr-nehmungsspezifikationen sind die Voraussetzung für eine anschließende Übersetzung in physikalische Schwingungsparameter. Plausible Vibratio-nen können synthetisiert werden, indem die erwarteten Wahrnehmungs-merkmale hervorgerufen werden. Auf der Grundlage der beobachteten Beziehungen zwischen Schwingungs¬parametern und sensorisch-taktilen Wahrnehmungsmerkmalen wurden ein 1-Nearest-Neighbor-Modell und ein Regressionsmodell erstellt. Die Plausibilität der von diesen Modellen synthetisierten Schwingungen im Kontext virtueller, auditorisch-visuell-taktiler Fahrzeugszenen wurde in einer Wahrnehmungsstudie validiert. Die Ergebnisse zeigten, dass die mit der Designsprache gewonnenen Wahr-nehmungsspezifikationen ausreichen, um Schwingungen zu synthetisieren, die in einem gegebenen Situationskontext als ebenso plausibel empfunden werden wie aufgezeichnete Schwingungen. Die demonstrierte Entwurfsme-thode stellt ein neues, effizienteres Werkzeug für Designer dar, die Schwingungen für virtuelle Umgebungen erstellen oder taktiles Feedback für Produkte erzeugen.:Preface III Abstract V Zusammenfassung VII List of Abbreviations XV 1 Introduction 1 1.1 General Introduction 1 1.1 Objectives of the Thesis 4 1.2 Structure of the Thesis 4 2. Tactile Perception in Real and Virtual Environments 7 2.1 Tactile Perception as a Multilayered Process 7 2.1.1 Physical Layer 8 2.1.2 Mechanoreceptor Layer 9 2.1.3 Sensory Layer 19 2.1.4 Affective Layer 26 2.2 Perception of Virtual Environments 29 2.2.1 The Place Illusion 29 2.2.2 The Plausibility Illusion 31 2.3 Approaches for the Authoring of Vibrations 38 2.3.1 Approaches on the Physical Layer 38 2.3.2 Approaches on the Mechanoreceptor Layer 40 2.3.3 Approaches on the Sensory Layer 40 2.3.4 Approaches on the Affective Layer 43 2.4 Summary 43 3. Research Concept 47 3.1 Research Questions 47 3.1.1 Foundations of the Research Concept 47 3.1.2 Research Concept 49 3.2 Limitations 50 4. Development of the Experimental Setup 53 4.1 Hardware 53 4.1.1 Optical Reproduction System 53 4.1.2 Acoustical Reproduction System 54 4.1.3 Whole-Body Vibration Reproduction System 56 4.2 Software 64 4.2.1 Combination of Reproduction Systems for Unimodal and Multimodal Presentation 64 4.2.2 Conducting Perceptual Studies 65 5. Assessment of a Sensory Tactile Design Language for Characterizing Vibration 67 5.1.1 Design Language Requirements 67 5.1.2 Method to Assess the Design Language 69 5.1.3 Goals of this Chapter 70 5.2 Tactile Stimuli 72 5.2.1 Generalization into Excitation Patterns 72 5.2.2 Definition of Parameter Values of the Excitation Patterns 75 5.2.3 Generation of the Stimuli 85 5.2.4 Summary 86 5.3 Assessment of the most relevant Sensory Tactile Perceptual Attributes 86 5.3.1 Experimental Design 87 5.3.2 Participants 88 5.3.3 Results 88 5.3.4 Aggregation and Prioritization 89 5.3.5 Summary 91 5.4 Identification of the Attributes forming the Design Language 92 5.4.1 Experimental Design 93 5.4.2 Participants 95 5.4.3 Results 95 5.4.4 Selecting the Elements of the Sensory Tactile Design Language 106 5.4.5 Summary 109 5.5 Summary and Discussion 109 5.5.1 Summary 109 5.5.2 Discussion 111 6. Quantification of Expected Properties with the Sensory Tactile Design Language 115 6.1 Multimodal Stimuli 116 6.1.1 Selection of the Scenes 116 6.1.2 Recording of the Scenes 117 6.1.3 Recorded Stimuli 119 6.2 Qualitative Communication in the Presence of Vibration 123 6.2.1 Experimental Design 123 6.2.2 Participants 124 6.2.3 Results 124 6.2.4 Summary 126 6.3 Quantitative Communication in the Presence of Vibration 126 6.3.1 Experimental Design 127 6.3.2 Participants 127 6.3.3 Results 127 6.3.4 Summary 129 6.4 Quantitative Communication in the Absence of Vibration 129 6.4.1 Experimental Design 130 6.4.2 Participants 132 6.4.3 Results 132 6.4.4 Summary 134 6.5 Summary and Discussion 135 7. Synthesis Models for the Translation of Sensory Tactile Properties into Vibration 137 7.1 Formalization of the Tactile Plausibility Illusion for Models 139 7.1.1 Formalization of Plausibility 139 7.1.2 Model Boundaries 143 7.2 Investigation of the Influence of Vibration Level on Attribute Ratings 144 7.2.1 Stimuli 145 7.2.2 Experimental Design 145 7.2.3 Participants 146 7.2.4 Results 146 7.2.5 Summary 148 7.3 Comparison of Modulated Vibration to Successive Impulse-like Vibration 148 7.3.1 Stimuli 149 7.3.2 Experimental Design 151 7.3.3 Participants 151 7.3.4 Results 151 7.3.5 Summary 153 7.4 Synthesis Based on the Discrete Estimates of a k-Nearest-Neighbor Classifier 153 7.4.1 Definition of the K-Nearest-Neighbor Classifier 154 7.4.2 Analysis Model 155 7.4.3 Synthesis Model 156 7.4.4 Interpolation of acceleration level for the vibration attribute profile pairs 158 7.4.5 Implementation of the Synthesis 159 7.4.6 Advantages and Disadvantages 164 7.5 Synthesis Based on the Quasi-Continuous Estimates of Regression Models 166 7.5.1 Overall Model Structure 168 7.5.2 Classification of the Excitation Pattern with a Support Vector Machine 171 7.5.3 General Approach to the Regression Models of each Excitation Pattern 178 7.5.4 Synthesis for the Impulse-like Excitation Pattern 181 7.5.5 Synthesis for the Bandlimited White Gaussian Noise Excitation Pattern 187 7.5.6 Synthesis for the Amplitude Modulated Sinusoidal Excitation Pattern 193 7.5.7 Synthesis for the Sinusoidal Excitation Pattern 199 7.5.8 Implementation of the Synthesis 205 7.5.9 Advantages and Disadvantages of the Approach 208 7.6 Validation of the Synthesis Models 210 7.6.1 Stimuli 212 7.6.2 Experimental Design 212 7.6.3 Participants 214 7.6.4 Results 214 7.6.5 Summary 219 7.7 Summary and Discussion 219 7.7.1 Summary 219 7.7.2 Discussion 222 8. General Discussion and Outlook 227 Acknowledgment 237 References 23

Time-ordered data simulation and map-making for the PIXIE Fourier transform spectrometer

We develop a time-ordered data simulator and map-maker for the proposed PIXIE Fourier transform spectrometer and use them to investigate the impact of polarization leakage, imperfect collimation, elliptical beams, sub-pixel effects, correlated noise and spectrometer mirror jitter on the PIXIE data analysis. We find that PIXIE is robust to all of these effects, with the exception of mirror jitter which could become the dominant source of noise in the experiment if the jitter is not kept significantly below $0.1\mu m\sqrt{s}$. Source code is available at https://github.com/amaurea/pixie.Comment: 27 pages, 15 figures. Accepted for publication in JCA

Roadmap on Superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments

Bandpass filters for unconstrained target recognition and their implementation in coherent optical correlators

An up-dateable correlator is simulated which is based on the non-degenerate four wave mixing (NDFWM) interaction in the photorefractive material bismuth silicon oxide (Bi12SiO20). Specifically, it is shown that variable bandpass filters can be implemented directly in the correlator by adjusting the relative strengths of the signal and reference beams used to write the Fourier transform hologram into the photorefractive. The synthetic discriminant function (SDF) method of grey-level multiplexing is reviewed. A bandpass modification of this technique is used in the design of a multiplexed filter for the recognition of an industrial test component from a limited number of known stable state orientations when viewed from an overhead camera position. Its performance in this task when implemented in the up-dateable correlator is assessed through simulation. The conclusion of this work is that filter multiplexing must be used judiciously for orientation invariant recognition. Only a limited number of images, typically under ten, may be multiplexed into each filter since correlation peak heights and peak-to-sidelobe ratios inevitably progressively deteriorate as images are added to the filter. The effect of severe amplitude disruptions in the frequency plane on correlation peak localisation is examined. In two or higher dimensions simulations show the localisation is very robust to this disruption; an analysis is developed to indicate the reason for this. The effect is exploited by the implementation of an algorithm that locally removes the spatial frequencies that exhibit close phase matching between intra- and inter-class images. The inter-class response can be forced to zero while simultaneously improving the intra-class tolerance to orientation changes. The technique is assessed through simulation with images of two types of motor vehicle, in a variety of orientations, and shown to be effective in improving discrimination and intra-class tolerance for examples in which these were initially very poor. Bandpass filters are experimentally implemented in a joint transform correlator (JTC) based on a NDFWM interaction in Bi12SiO20. The JTC is described and its full bandwidth performance initially assessed. As anticipated from the previous considerations, inter-class discrimination was high but the intra-class tolerance very poor due to the high sensitivity of the filter. The difference of Gaussian approximation to a Laplacian of a Gaussian filter is described and its experimental implementation in the JTC detailed. Experimental results are presented for the orientation independent recognition of a car while maintaining discrimination against another car. An intra-class to inter-class correlation ratio of 7.5 dB was obtained as a best case and 3.6 dB as a worst case, the intra-class variation being at 11 ° increments in orientation at zero elevation angle. The results are extrapolated to estimate that approximately 80 filters would be required for a full 2 steradian orientation coverage. The implementation of the frequency removal technique and the Wiener filter in the JTC is briefly considered in conclusion to this work

Roadmap on superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments