Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation

An alternative to conventional uniform sampling is that of time encoding, which converts continuous-time signals into streams of trigger times. This gives rise to Event-Driven Sampling (EDS) models. The data-driven nature of EDS acquisition is advantageous in terms of power consumption and time resolution and is inspired by the information representation in biological nervous systems. If an analog signal is outside a predefined dynamic range, then EDS generates a low density of trigger times, which in turn leads to recovery distortion due to aliasing. In this paper, inspired by the Unlimited Sensing Framework (USF), we propose a new EDS architecture that incorporates a modulo nonlinearity prior to acquisition that we refer to as the modulo EDS or MEDS. In MEDS, the modulo nonlinearity folds high dynamic range inputs into low dynamic range amplitudes, thus avoiding recovery distortion. In particular, we consider the asynchronous sigma-delta modulator (ASDM), previously used for low power analog-to-digital conversion. This novel MEDS based acquisition is enabled by a recent generalization of the modulo nonlinearity called modulo-hysteresis. We design a mathematically guaranteed recovery algorithm for bandlimited inputs based on a sampling rate criterion and provide reconstruction error bounds. We go beyond numerical experiments and also provide a first hardware validation of our approach, thus bridging the gap between theory and practice, while corroborating the conceptual underpinnings of our work.Comment: 27 pgs, 11 figures, IEEE Trans. Sig. Proc., accepted with minor revision

Fault-Tolerant Torque Control Based on Common and Differential Mode Modeling for Multi-Three-Phase Induction Machines

Among the multiphase solutions, multi-three-phase drives are experiencing significant industrial development since they can be configured as multiple three-phase units operating in parallel. The literature reports several control approaches to perform the torque regulation of multi-three-phase machines. Most of such solutions use the vector space decomposition (VSD) approach since it allows the control of a multi-three-phase machine using the conventional control schemes of three-phase drives, reducing the complexity of the control algorithm. However, this advantage is practically lost in the case of open-three-phase faults. Indeed, the post-fault operation of the VSD-based drive schemes requires the implementation of additional control modules, often specifically designed for the machine under consideration. Therefore, this paper aims at proposing a novel control approach that allows using any control scheme developed for three-phase motors to perform the torque regulation of a multi-three-phase machine both in healthy and faulty operation. In this way, the previously mentioned drawbacks of the VSD-based control schemes in dealing with the machine's faulty operation are avoided. Moreover, the simplicity of the control algorithm is always preserved regardless of the machine operating condition. The proposed solution has been experimentally validated through a 12-phase induction motor, rated 10 kW at 6000 r/min, which uses a quadruple-three-phase configuration of the stator winding

Fault-Tolerant Torque Controller Based on Adaptive Decoupled Multi-Stator Modeling for Multi-Three-Phase Induction Motor Drives

Among the multiphase solutions, multi-three-phase drives are becoming more and more widespread in practice as they can be modularly supplied by conventional three-phase inverters. The literature reports several control approaches to perform the torque regulation of multi-three-phase machines. Most of such solutions use the vector space decomposition (VSD) approach since it allows the control of a multi-three-phase machine using the conventional control schemes of three-phase drives, thus reducing the complexity of the control algorithm. However, this advantage is practically lost in the case of open-three-phase faults. Indeed, the postfault operation of the VSD-based drive schemes requires the implementation of additional control modules, often specifically designed for the machine under consideration. Therefore, this article aims to propose a novel control approach that allows using any control scheme developed for three-phase motors to perform the torque regulation of a multi-three-phase machine both in healthy and faulty operation. In this way, the previously mentioned drawbacks of the VSD-based control schemes in dealing with the faulty operation of the machine are avoided. Moreover, the simplicity of the control algorithm is always preserved, regardless of the machine's operating condition. The proposed solution has been experimentally validated through a 12-phase induction motor, rated 10 kW at 6000 r/min, using a quadruple-three-phase configuration of the stator winding

Asynchronous Signal Processing for Compressive Data Transmission

In this thesis we propose a power-efficient procedure useful in the acquisition of biological data in digital form without using high frequency samplers. The data is compressed so that transmission is limited to parts of the signal that are significant. Our procedure uses an asynchronous sigma delta modulator (ASDM) together with a time-to-digital converter (TDC) to obtain binary data that is transmitted via orthogonal frequency division multiplexing (OFDM). The asynchronous sigma delta modulator is a nonlinear feedback system that allows the representation of bounded signals by zero-crossing times of a binary signal. Using duty-cycle modulation, the ASDM is shown to be equivalent to an optimal level-crossing sampler. The zero-crossing times are measured with a time-to-digital converter that applies pulse-shrinking delay lines and requires no high-frequency clock. Reconstruction of the original signal is possible from the zero-crossing times of the ASDM output binary signal. ASDM time-domain compression is compared with discrete wavelet transform based data compression. For wireless data transmission, the orthogonal frequency division multiplexing (OFDM) reduces the bit error-rate in multipath fading channels. The performance of the proposed algorithm is illustrated using an electrocardiogram signal, which fits the bursty characteristic appropriate for our procedure

Fault-Tolerant Torque Controller Based on Adaptive Decoupled Multi-Stator Modeling for Multi-Three-Phase Induction Motor Drives

Among the multiphase solutions, multi-three- phase drives are becoming more and more widespread in practice as they can be modularly supplied by conventional three-phase inverters. The literature reports several control approaches to perform the torque regulation of multi-three- phase machines. Most of such solutions use the vector space decomposition (VSD) approach since it allows the control of a multi-three-phase machine using the conventional control schemes of three-phase drives, thus reducing the complexity of the control algorithm. However, this advantage is practically lost in the case of open-three-phase faults. Indeed, the post-fault operation of the VSD-based drive schemes requires the implementation of additional control modules, often specifically designed for the machine under consideration. Therefore, this paper aims to propose a novel control approach that allows using any control scheme developed for three-phase motors to perform the torque regulation of a multi-three-phase machine both in healthy and faulty operation. In this way, the previously mentioned drawbacks of the VSD-based control schemes in dealing with the faulty operation of the machine are avoided. Moreover, the simplicity of the control algorithm is always preserved, regardless of the machine's operating condition. The proposed solution has been experimentally validated through a 12-phase induction motor, rated 10 kW at 6000 r/min, using a quadruple-three-phase configuration of the stator windin

Identification of Dendritic Processing in Spiking Neural Circuits

A large body of experimental evidence points to sophisticated signal processing taking place at the level of dendritic trees and dendritic branches of neurons. This evidence suggests that, in addition to inferring the connectivity between neurons, identifying analog dendritic processing in individual cells is fundamentally important to understanding the underlying principles of neural computation. In this thesis, we develop a novel theoretical framework for the identification of dendritic processing directly from spike times produced by spiking neurons. The problem setting of spiking neurons is necessary since such neurons make up the majority of electrically excitable cells in most nervous systems and it is often hard or even impossible to directly monitor the activity within dendrites. Thus, action potentials produced by neurons often constitute the only causal and observable correlate of dendritic processing. In order to remain true to the underlying biophysics of electrically excitable cells, we employ well-established mechanistic models of action potential generation to describe the nonlinear mapping of the aggregate current produced by the tree into an asynchronous sequence of spikes. Specific models of spike generation considered include conductance-based models such as Hodgkin-Huxley, Morris-Lecar, Fitzhugh-Nagumo, as well as simpler models of the integrate-and-fire and threshold-and-fire type. The aggregate time-varying current driving the spike generator is taken to be produced by a dendritic stimulus processor, which is a nonlinear dynamical system capable of describing arbitrary linear and nonlinear transformations performed on one or more input stimuli. In the case of multiple stimuli, it can also describe the cross-coupling, or interaction, between various stimulus features. The behavior of the dendritic stimulus processor is fully captured by one or more kernels, which provide a characterization of the signal processing that is consistent with the broader cable theory description of dendritic trees. We prove that the neural identification problem, stated in terms of identifying the kernels of the dendritic stimulus processor, is mathematically dual to the neural population encoding problem. Specifically, we show that the collection of spikes produced by a single neuron in multiple experimental trials can be treated as a single multidimensional spike train of a population of neurons encoding the parameters of the dendritic stimulus processor. Using the theory of sampling in reproducing kernel Hilbert spaces, we then derive precise results demonstrating that, during any experiment, the entire neural circuit is projected onto the space of input stimuli and parameters of this projection are faithfully encoded in the spike train. Spike times are shown to correspond to generalized samples, or measurements, of this projection in a system of coordinates that is not fixed but is both neuron- and stimulus-dependent. We examine the theoretical conditions under which it may be possible to reconstruct the dendritic stimulus processor from these samples and derive corresponding experimental conditions for the minimum number of spikes and stimuli that need to be used. We also provide explicit algorithms for reconstructing the kernel projection and demonstrate that, under natural conditions, this projection converges to the true kernel. The developed methodology is quite general and can be applied to a number of neural circuits. In particular, the methods discussed span all sensory modalities, including vision, audition and olfaction, in which external stimuli are typically continuous functions of time and space. The results can also be applied to circuits in higher brain centers that receive multi-dimensional spike trains as input stimuli instead of continuous signals. In addition, the modularity of the approach allows one to extend it to mixed-signal circuits processing both continuous and spiking stimuli, to circuits with extensive lateral connections and feedback, as well as to multisensory circuits concurrently processing multiple stimuli of different dimensions, such as audio and video. Another important extension of the approach can be used to estimate the phase response curves of a neuron. All of the theoretical results are accompanied by detailed examples demonstrating the performance of the proposed identification algorithms. We employ both synthetic and naturalistic stimuli such as natural video and audio to highlight the power of the approach. Finally, we consider the implication of our work on problems pertaining to neural encoding and decoding and discuss promising directions for future research

Multiple-Resonator Wireless Power Transmission System Design and Integrated Data Path

With the rapid development of mobile and implantable devices, the wireless power transfer (WPT) technology has become increasingly attractive because it frees numerous electronic systems from power cords or batteries. Recently, the WPT method based on the magnetic resonant coupling has gained popularity both in research and applications. This dissertation contributes to the magnetic resonant WPT system design by addressing three important problems. The first problem deals with the design of multiple-resonator systems. In order to power objects over a longer distance, a multiple-resonator system is usually needed. However, most existing multiple-resonator systems are designed experimentally with a strict requirement on the position of the resonators. We propose to optimize multiple-resonator systems by investigating the transfer function from the transmitter to the receiver. An equivalent circuit model is developed to maximize the power output. This method is then utilized to find the optimal position for the relay resonator in a three-resonator wireless power transfer system. The second problem is to power a device which is mobile within a certain field. The Biot-Savart law and a concentric model of a spiral coil are utilized to simulate the magnetic field distribution of a multiple-transmitter WPT platform. The vertical component of the magnetic field of the coil is optimized to achieve an evenly distributed magnetic field over the field. As a result, a position-free powering of mobile sensors or devices is achieved. The third problem deals with integration of wireless power transfer and wireless data communication. This problem is especially importation in implanted medical sensors where power must be delivered to the implants and measured data must be transmitted to the outside of the human body. Currently, most implementations of power and communication systems utilize a separated data channel, which requires not only substantial power consumption but also a high complexity of the implanted circuit. In this work, a unified data and power channel is developed in which data are processed by an asynchronous sigma-delta pulse conversion. The resulting pulses are transmitted using load modulation

Asynchronous spike event coding scheme for programmable analogue arrays and its computational applications

This work is the result of the definition, design and evaluation of a novel method to interconnect the computational elements - commonly known as Configurable Analogue Blocks (CABs) - of a programmable analogue array. This method is proposed for total or partial replacement of the conventional methods due to serious limitations of the latter in terms of scalability. With this method, named Asynchronous Spike Event Coding (ASEC) scheme, analogue signals from CABs outputs are encoded as time instants (spike events) dependent upon those signals activity and are transmitted asynchronously by employing the Address Event Representation (AER) protocol. Power dissipation is dependent upon input signal activity and no spike events are generated when the input signal is constant. On-line, programmable computation is intrinsic to ASEC scheme and is performed without additional hardware. The ability of the communication scheme to perform computation enhances the computation power of the programmable analogue array. The design methodology and a CMOS implementation of the scheme are presented together with test results from prototype integrated circuits (ICs)

Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application

Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants

Reconstruction, identification and implementation methods for spiking neural circuits

Integrate-and-fire (IF) neurons are time encoding machines (TEMs) that convert the amplitude of an analog signal into a non-uniform, strictly increasing sequence of spike times. This thesis addresses three major issues in the field of computational neuroscience as well as neuromorphic engineering. The first problem is concerned with the formulation of the encoding performed by an IF neuron. The encoding mechanism is described mathematically by the t-transform equation, whose standard formulation is given by the projection of the stimulus onto a set of input dependent frame functions. As a consequence, the standard methods reconstruct the input of an IF neuron in a space spanned by a set of functions that depend on the stimulus. The process becomes computationally demanding when performing reconstruction from long sequences of spike times. The issue is addressed in this work by developing a new framework in which the IF encoding process is formulated as a problem of uniform sampling on a set of input independent time points. Based on this formulation, new algorithms are introduced for reconstructing the input of an IF neuron belonging to bandlimited as well as shift-invariant spaces. The algorithms are significantly faster, whilst providing a similar level of accuracy, compared to the standard reconstruction methods. Another important issue calls for inferring mathematical models for sensory processing systems directly from input-output observations. This problem was addressed before by performing identification of sensory circuits consisting of linear filters in series with ideal IF neurons, by reformulating the identification problem as one of stimulus reconstruction. The result was extended to circuits in which the ideal IF neuron was replaced by more biophysically realistic models, under the additional assumptions that the spiking neuron parameters are known a priori, or that input-output measurements of the spiking neuron are available. This thesis develops two new identification methodologies for [Nonlinear Filter]-[Ideal IF] and [Linear Filter]-[Leaky IF] circuits consisting of two steps: the estimation of the spiking neuron parameters and the identification of the filter. The methodologies are based on the reformulation of the circuit as a scaled filter in series with a modified spiking neuron. The first methodology identifies an unknown [Nonlinear Filter]-[Ideal IF] circuit from input-output data. The scaled nonlinear filter is estimated using the NARMAX identification methodology for the reconstructed filter output. The [Linear Filter]-[Leaky IF] circuit is identified with the second proposed methodology by first estimating the leaky IF parameters with arbitrary precision using specific stimuli sequences. The filter is subsequently identified using the NARMAX identification methodology. The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain. In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train