Economical sampling of parametric signals

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 107-115).This thesis proposes architectures and algorithms for digital acquisition of parametric signals. It furthermore provides bounds for the performance of these systems in the presence of noise. Our simple acquisition circuitry and low sampling rate enable accurate parameter estimation to be achieved economically. In present practice, sampling and estimation are not integrated: the sampling device does not take advantage of the parametric model, and the estimation assumes that noise in the data is signal-independent additive white Gaussian noise. We focus on estimating the timing information in signals that are linear combinations of scales and shifts of a known pulse. This signal model is well-known in a variety of disciplines such as ultra-wideband signaling, neurobiology, etc. The signal is completely determined by the amplitudes and shifts of the summands. The delays determine a subspace that contains the signals, so estimating the shifts is equivalent to subspace estimation. By contrast, conventional sampling theory yields a least-squares approximation to a signal from a fixed shift-invariant subspace of possible reconstructions. Conventional acquisition takes samples at a rate higher than twice the signal bandwidth.(cont.) Although this may be feasible, there is a trade-off between power, accuracy, and speed. Under the signal model of interest, when the pulses are very narrow, the number of parameters per unit time-the rate of innovation-is much lower than the Fourier bandwidth. There is thus potential for much lower sampling rate so long as nonlinear reconstruction algorithms are used. We present a new sampling scheme that takes simultaneous samples at the outputs of multiple channels. This new scheme can be implemented with simple circuitry and has a successive approximation property that can be used to detect undermodeling. In many regimes our algorithms provide better timing accuracy and resolution than conventional systems. Our new analytical and algorithmic techniques are applied to previously proposed systems, and it is shown that all the systems considered have super-resolution properties. Finally, we consider the same parameter estimation problem when the sampling instances are perturbed by signal-independent timing noise. We give an iterative algorithm that achieves accurate timing estimation by exploiting knowledge of the pulse shape.by Julius Kusuma.Ph.D

An Improved Shashlyk Calorimeter

Shashlyk electromagnetic calorimeter modules with an energy resolution of about 3%/sqrt{E (GeV)} for 50-1000 MeV photons has been developed, and a prototype tested. Details of these improved modules, including mechanical construction, selection of wave shifting fibers and photo-detectors, and development of a new scintillator with improved optical and mechanical properties are described. How the modules will perform in a large calorimeter was determined from prototype measurements. The experimentally determined characteristics of the calorimeter prototype show energy resolution of sigma_E/E=(1.96+-0.1)% \oplus (2.74+-0.05)%/sqrt{E}, time resolution of sigma_T = (72+-4)/sqrt{E} \oplus (14+-2)/E (ps), where photon energy E is given in GeV units and \oplus means a quadratic summation. A punch-through inefficiency of photon detection was measured to be \epsilon = 5*10^{-5} (\Theta >5 mrad).Comment: 29 pages, 21 figure

Local-set-based Graph Signal Reconstruction

Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the graph signal. In this paper, the concept of local set is introduced and two local-set-based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, one of the proposed methods reweights the sampled residuals for different vertices, while the other propagates the sampled residuals in their respective local sets. These algorithms are built on frame theory and the concept of local sets, based on which several frames and contraction operators are proposed. We then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method. Furthermore, the correspondence between graph signal sampling and time-domain irregular sampling is analyzed comprehensively, which may be helpful to future works on graph signals. Computer simulations are conducted. The experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries, imprecise priori knowledge of cutoff frequency, and noisy scenarios.Comment: 28 pages, 9 figures, 6 tables, journal manuscrip

Detection of time reversibility in time series by ordinal patterns analysis

Time irreversibility is a common signature of nonlinear processes, and a fundamental property of non-equilibrium systems driven by non-conservative forces. A time series is said to be reversible if its statistical properties are invariant regardless of the direction of time. Here we propose the Time Reversibility from Ordinal Patterns method (TiROP) to assess time-reversibility from an observed finite time series. TiROP captures the information of scalar observations in time forward, as well as its time-reversed counterpart by means of ordinal patterns. The method compares both underlying information contents by quantifying its (dis)-similarity via Jensen-Shannon divergence. The statistic is contrasted with a population of divergences coming from a set of surrogates to unveil the temporal nature and its involved time scales. We tested TiROP in different synthetic and real, linear and non linear time series, juxtaposed with results from the classical Ramsey's time reversibility test. Our results depict a novel, fast-computation, and fully data-driven methodology to assess time-reversibility at different time scales with no further assumptions over data. This approach adds new insights about the current non-linear analysis techniques, and also could shed light on determining new physiological biomarkers of high reliability and computational efficiency.Comment: 8 pages, 5 figures, 1 tabl

Hardware prototyping and validation of a W-ΔDOR digital signal processor

Microwave tracking, usually performed by on ground processing of the signals coming from a spacecraft, represents a crucial aspect in every deep-space mission. Various noise sources, including receiver noise, affect these signals, limiting the accuracy of the radiometric measurements obtained from the radio link. There are several methods used for spacecraft tracking, including the Delta-Differential One-Way Ranging (ΔDOR) technique. In the past years, European Space Agency (ESA) missions relied on a narrowband ΔDOR system for navigation in the cruise phase. To limit the adverse effect of nonlinearities in the receiving chain, an innovative wideband approach to ΔDOR measurements has recently been proposed. This work presents the hardware implementation of a new version of the ESA X/Ka Deep Space Transponder based on the new tracking technique named Wideband ΔDOR (W-ΔDOR). The architecture of the new transponder guarantees backward compatibility with narrowband ΔDOR

A Distributed Tracking Algorithm for Reconstruction of Graph Signals

The rapid development of signal processing on graphs provides a new perspective for processing large-scale data associated with irregular domains. In many practical applications, it is necessary to handle massive data sets through complex networks, in which most nodes have limited computing power. Designing efficient distributed algorithms is critical for this task. This paper focuses on the distributed reconstruction of a time-varying bandlimited graph signal based on observations sampled at a subset of selected nodes. A distributed least square reconstruction (DLSR) algorithm is proposed to recover the unknown signal iteratively, by allowing neighboring nodes to communicate with one another and make fast updates. DLSR uses a decay scheme to annihilate the out-of-band energy occurring in the reconstruction process, which is inevitably caused by the transmission delay in distributed systems. Proof of convergence and error bounds for DLSR are provided in this paper, suggesting that the algorithm is able to track time-varying graph signals and perfectly reconstruct time-invariant signals. The DLSR algorithm is numerically experimented with synthetic data and real-world sensor network data, which verifies its ability in tracking slowly time-varying graph signals.Comment: 30 pages, 9 figures, 2 tables, journal pape

Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction

Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite their common use, however, practical guidelines for the choice of wavelet method, filter, and length have remained largely undelineated. Here, we explicitly explore the effects of wavelet method (MODWT vs. DWT), wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families), and wavelet length (2 to 24) - each essential parameters in wavelet-based methods - on the estimated values of network diagnostics and in their sensitivity to alterations in psychiatric disease. We observe that the MODWT method produces less variable estimates than the DWT method. We also observe that the length of the wavelet filter chosen has a greater impact on the estimated values of network diagnostics than the type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of the method to detect differences between health and disease and tunes classification accuracy. Collectively, our results suggest that the choice of wavelet method and length significantly alters the reliability and sensitivity of these methods in estimating values of network diagnostics drawn from graph theory. They furthermore demonstrate the importance of reporting the choices utilized in neuroimaging studies and support the utility of exploring wavelet parameters to maximize classification accuracy in the development of biomarkers of psychiatric disease and neurological disorders.Comment: working pape