Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses

The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise.We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise.We denote the resulting algorithm as vector fitting with adding and skimming (VF-AS). A thorough validation of the VF-AS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VF-AS algorithm to measured scattering responses of interconnect structures and networks typical of high-speed digital systems

Quantum field tomography

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.Comment: 31 pages, 5 figures, minor change

Regular sparse array direction of arrival estimation in one dimension

Traditionally regularly spaced antenna arrays follow the spatial Nyquist criterion to guarantee an unambiguous analysis. We present a novel technique that makes use of two sparse non-Nyquist regularly spaced antenna arrays, where one of the arrays is just a shifted version of the other. The method offers several advantages over the use of traditional dense Nyquist spaced arrays, while maintaining a comparable algorithmic complexity for the analysis. Among the advantages we mention: an improved resolution for the same number of receivers and reduced mutual coupling effects between the receivers, both due to the increased separation between the antennas. Because of a shared structured linear system of equations between the two arrays, as a consequence of the shift between the two, the analysis of both is automatically paired, thereby avoiding a computationally expensive matching step as is required in the use of so-called co-prime arrays. In addition, an easy validation step allows to automatically detect the precise number of incoming signals, which is usually considered a difficult issue. At the same time, the validation step improves the accuracy of the retrieved results and eliminates unreliable results in the case of noisy data. The performance of the proposed method is illustrated with respect to the influence of noise as well to the effect of mutual coupling

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Universality and scaling behavior of RG gauge actions

We study universality and scaling properties of RG gauge actions (Iwasaki and DBW2). In the first part we consider the critical temperature T_{c} and compute the reference energy scale r_{0} for critical couplings \beta_{c} corresponding to N_{t}=3,4,6,8. The universality of T_{c}r_{0} between Iwasaki and Wilson action is confirmed and the scaling behavior of the Iwasaki action is found to be better than the one for the Wilson action. The results for the DBW2 action show larger lattice artefacts. A continuum value T_{c}r_{0}=0.7498(50) is extracted. We compute also the glueball masses for the states 0^{++} and 2^{++}, investigate the scaling of m_{0^{++}}r_{0} and m_{2^{++}}r_{0} and point out practical problems which are due to the violation of positivity present in the RG actions.Comment: 36 page

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Decimated generalized Prony systems

We continue studying robustness of solving algebraic systems of Prony type (also known as the exponential fitting systems), which appear prominently in many areas of mathematics, in particular modern "sub-Nyquist" sampling theories. We show that by considering these systems at arithmetic progressions (or "decimating" them), one can achieve better performance in the presence of noise. We also show that the corresponding lower bounds are closely related to well-known estimates, obtained for similar problems but in different contexts

Modeling and frequency tracking of marine mammal whistle calls

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2009Marine mammal whistle calls present an attractive medium for covert underwater communications. High quality models of the whistle calls are needed in order to synthesize natural-sounding whistles with embedded information. Since the whistle calls are composed of frequency modulated harmonic tones, they are best modeled as a weighted superposition of harmonically related sinusoids. Previous research with bottlenose dolphin whistle calls has produced synthetic whistles that sound too “clean” for use in a covert communications system. Due to the sensitivity of the human auditory system, watermarking schemes that slightly modify the fundamental frequency contour have good potential for producing natural-sounding whistles embedded with retrievable watermarks. Structured total least squares is used with linear prediction analysis to track the time-varying fundamental frequency and harmonic amplitude contours throughout a whistle call. Simulation and experimental results demonstrate the capability to accurately model bottlenose dolphin whistle calls and retrieve embedded information from watermarked synthetic whistle calls. Different fundamental frequency watermarking schemes are proposed based on their ability to produce natural sounding synthetic whistles and yield suitable watermark detection and retrieval