Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Micromachined vibratory gyroscopes controlled by a high order band-pass sigma delta modulator.

Abstract—This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (SDM). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass SDM’s. Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude- modulated signal. Therefore, a bandpass M is a more appropriate control strategy for a vibratory gyroscope than a low-pass SDM. Using a high-order bandpass SDM, the control system can adopt a much lower sampling frequency compared with a low-pass SDM while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass SDM is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order SDM control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level

Sampling from a system-theoretic viewpoint: Part II - Noncausal solutions

This paper puts to use concepts and tools introduced in Part I to address a wide spectrum of noncausal sampling and reconstruction problems. Particularly, we follow the system-theoretic paradigm by using systems as signal generators to account for available information and system norms (L2 and L∞) as performance measures. The proposed optimization-based approach recovers many known solutions, derived hitherto by different methods, as special cases under different assumptions about acquisition or reconstructing devices (e.g., polynomial and exponential cardinal splines for fixed samplers and the Sampling Theorem and its modifications in the case when both sampler and interpolator are design parameters). We also derive new results, such as versions of the Sampling Theorem for downsampling and reconstruction from noisy measurements, the continuous-time invariance of a wide class of optimal sampling-and-reconstruction circuits, etcetera

Multichannel Sampling of Pulse Streams at the Rate of Innovation

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches

A VHDL-AMS Simulation Environment for an UWB Impulse Radio Transceiver

Ultra-Wide-Band (UWB) communication based on the impulse radio paradigm is becoming increasingly popular. According to the IEEE 802.15 WPAN Low Rate Alternative PHY Task Group 4a, UWB will play a major role in localization applications, due to the high time resolution of UWB signals which allow accurate indirect measurements of distance between transceivers. Key for the successful implementation of UWB transceivers is the level of integration that will be reached, for which a simulation environment that helps take appropriate design decisions is crucial. Owing to this motivation, in this paper we propose a multiresolution UWB simulation environment based on the VHDL-AMS hardware description language, along with a proper methodology which helps tackle the complexity of designing a mixed-signal UWB System-on-Chip. We applied the methodology and used the simulation environment for the specification and design of an UWB transceiver based on the energy detection principle. As a by-product, simulation results show the effectiveness of UWB in the so-called ranging application, that is the accurate evaluation of the distance between a couple of transceivers using the two-way-ranging metho

Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction