Efficient Sampling of Band-limited Signals from Sine Wave Crossings

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity in these converters. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the correspondence are validated in several numerical examples.Comment: To appear in the IEEE Transactions on Signal Processin

Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method

The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method.Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit-type algorithms.Comment: 14 pages, 23 figures, submitted to Astronomy and Astrophysic

Low-Computational-Cost Hybrid FEM-Analytical Induction Machine Model for the Diagnosis of Rotor Eccentricity, Based on Sparse Identification Techniques and Trigonometric Interpolation

[EN] Since it is not efficient to physically study many machine failures, models of faulty induction machines (IMs) have attracted a rising interest. These models must be accurate enough to include fault effects and must be computed with relatively low resources to reproduce different fault scenarios. Moreover, they should run in real time to develop online condition-monitoring (CM) systems. Hybrid finite element method (FEM)-analytical models have been recently proposed for fault diagnosis purposes since they keep good accuracy, which is widely accepted, and they can run in real-time simulators. However, these models still require the full simulation of the FEM model to compute the parameters of the analytical model for each faulty scenario with its corresponding computing needs. To address these drawbacks (large computing power and memory resources requirements) this paper proposes sparse identification techniques in combination with the trigonometric interpolation polynomial for the computation of IM model parameters. The proposed model keeps accuracy similar to a FEM model at a much lower computational effort, which could contribute to the development and to the testing of condition-monitoring systems. This approach has been applied to develop an IM model under static eccentricity conditions, but this may extend to other fault types.This work was supported by the Spanish "Ministerio de Ciencia, Innovacion y Universidades (MCIU)", the "Agencia Estatal de Investigacion (AEI)" and the "Fondo Europeo de Desarrollo Regional (FEDER)" in the framework of the "Proyectos I+D+i -Retos Investigacion 2018", project reference RTI2018-102175-B-I00 (MCIU/AEI/FEDER, UE).Terrón-Santiago, C.; Martinez-Roman, J.; Puche-Panadero, R.; Sapena-Bano, A. (2021). Low-Computational-Cost Hybrid FEM-Analytical Induction Machine Model for the Diagnosis of Rotor Eccentricity, Based on Sparse Identification Techniques and Trigonometric Interpolation. Sensors. 21(21):6963-6987. https://doi.org/10.3390/s21216963S69636987212

Low-Rank Univariate Sum of Squares Has No Spurious Local Minima

We study the problem of decomposing a polynomial $p$ into a sum of $r$ squares by minimizing a quadratically penalized objective $f_p(\mathbf{u}) = \left\lVert \sum_{i=1}^r u_i^2 - p\right\lVert^2$. This objective is nonconvex and is equivalent to the rank-$r$ Burer-Monteiro factorization of a semidefinite program (SDP) encoding the sum of squares decomposition. We show that for all univariate polynomials $p$, if $r \ge 2$ then $f_p(\mathbf{u})$ has no spurious second-order critical points, showing that all local optima are also global optima. This is in contrast to previous work showing that for general SDPs, in addition to genericity conditions, $r$ has to be roughly the square root of the number of constraints (the degree of $p$) for there to be no spurious second-order critical points. Our proof uses tools from computational algebraic geometry and can be interpreted as constructing a certificate using the first- and second-order necessary conditions. We also show that by choosing a norm based on sampling equally-spaced points on the circle, the gradient $\nabla f_p$ can be computed in nearly linear time using fast Fourier transforms. Experimentally we demonstrate that this method has very fast convergence using first-order optimization algorithms such as L-BFGS, with near-linear scaling to million-degree polynomials.Comment: 18 pages, to appear in SIAM Journal on Optimizatio

Hardward and algorithm architectures for real-time additive synthesis

Additive synthesis is a fundamental computer music synthesis paradigm tracing its origins to the work of Fourier and Helmholtz. Rudimentary implementation linearly combines harmonic sinusoids (or partials) to generate tones whose perceived timbral characteristics are a strong function of the partial amplitude spectrum. Having evolved over time, additive synthesis describes a collection of algorithms each characterised by the time-varying linear combination of basis components to generate temporal evolution of timbre. Basis components include exactly harmonic partials, inharmonic partials with time-varying frequency or non-sinusoidal waveforms each with distinct spectral characteristics. Additive synthesis of polyphonic musical instrument tones requires a large number of independently controlled partials incurring a large computational overhead whose investigation and reduction is a key motivator for this work. The thesis begins with a review of prevalent synthesis techniques setting additive synthesis in context and introducing the spectrum modelling paradigm which provides baseline spectral data to the additive synthesis process obtained from the analysis of natural sounds. We proceed to investigate recursive and phase accumulating digital sinusoidal oscillator algorithms, defining specific metrics to quantify relative performance. The concepts of phase accumulation, table lookup phase-amplitude mapping and interpolated fractional addressing are introduced and developed and shown to underpin an additive synthesis subclass - wavetable lookup synthesis (WLS). WLS performance is simulated against specific metrics and parameter conditions peculiar to computer music requirements. We conclude by presenting processing architectures which accelerate computational throughput of specific WLS operations and the sinusoidal additive synthesis model. In particular, we introduce and investigate the concept of phase domain processing and present several “pipeline friendly” arithmetic architectures using this technique which implement the additive synthesis of sinusoidal partials

Digital Low Level RF

The demand on high stability and precision on the RF voltage for modern accelerators, as well as better diagnostics, maintenance and flexibility is driving the community to develop Digital Low Level RF systems (DLLRF) for both linear accelerators and synchrotrons. The state of the art in digital technologies applied to DLLRF systems is reviewed; different designs developed or in development at various laboratories are surveyed

Investigation into PRS-precoded, constant-envelope, continuous-phase digital modulation schemes

Bibliography: leaves 78-79.Partial response signaling ( PRS) has been used successfully to improve the spectral properties of Pulse Amplitude Modulated (PAM) digital transmission systems. This thesis investigation studied the effect of PRS on frequency- and phase-modulated carrier systems, in particular on their spectral performance and their maintenance of constant envelope

Ionospheric Regional modeling Algorithm based on GNSS Precise Point Positioning

Precise point positioning (PPP) is an absolute spatial positioning technology different from carrier phase relative positioning. With the continuous development of Global navigation satellite system (GNSS), multi-constellation GNSS further provides PPP with more abundant observation information and useful spatial geometric observations, which improves positioning performance and robustness. In recent years, the un-difference and un-combined precise point positioning (UPPP) has been continuously developing. Firstly, we introduce the basic theory of GNSS positioning and compare the position performance between UPPP and ionospheric-free PPP (IF PPP). The positioning performance of the four mainstream GNSS systems, GPS, GLONASS, Galileo, and Beidou, the PPP floating-point solutions of the four satellite systems all converge within 60 minutes and their error are less than 10cm. Secondly, a two-dimensional (2-d) model is proposed to fit the vertical total electronic content (VTEC) in the ionosphere with the ionospheric delays extracted by UPPP. With the model constraining the ionospheric delay in UPPP, the convergence is 2 minutes shorter than using the global ionospheric map (GIM) from IGS. Thirdly, to solve the limitation of the traditional methods in 2d representation, a method is proposed represent the ionosphere in 3D, called Compressed Sensing Tomography (CST). Comparing the simulated single-difference slant total electron content (STEC) and the input single- difference STEC between satellites, the root mean square (RMS) of the reference station’s error is less than 1 TEC uni