Efficient and Accurate Frequency Estimation of Multiple Superimposed Exponentials in Noise

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm that estimates the frequency of each component iteratively and consecutively by combining an estimator with a leakage subtraction scheme. During the iterative process, the proposed method gradually reduces estimation error and improves the frequency estimation accuracy. We give theoretical analysis where we derive the theoretical bias and variance of the frequency estimates and discuss the convergence behaviour of the estimator. We show that the algorithm converges to the asymptotic fixed point where the estimation is asymptotically unbiased and the variance is just slightly above the Cramer-Rao lower bound. We then verify the theoretical results and estimation performance using extensive simulation. The simulation results show that the proposed algorithm is capable of obtaining more accurate estimates than state-of-art methods with only a few iterations.Comment: 10 pages, 10 figure

Assessment of stochastic and deterministic models of 6304 quasar lightcurves from SDSS Stripe 82

The optical light curves of many quasars show variations of tenths of a magnitude or more on time scales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of over 20 deterministic and stochastic models on 6304 QSO light curves in SDSS Stripe 82. We include the damped random walk (or Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model which recent studies have focused on. Further models we consider are single and double sinusoids, multiple OU processes, higher order continuous autoregressive processes, and composite models. We find that only 29 out of 6304 QSO lightcurves are described significantly better by a deterministic model than a stochastic one. The OU process is an adequate description of the vast majority of cases (6023). Indeed, the OU process is the best single model for 3462 light curves, with the composite OU process/sinusoid model being the best in 1706 cases. The latter model is the dominant one for brighter/bluer QSOs. Furthermore, a non-negligible fraction of QSO lightcurves show evidence that not only the mean is stochastic but the variance is stochastic, too. Our results confirm earlier work that QSO light curves can be described with a stochastic model, but place this on a firmer footing, and further show that the OU process is preferred over several other stochastic and deterministic models. Of course, there may well exist yet better (deterministic or stochastic) models which have not been considered here.Comment: accepted by AA, 12 pages, 11 figures, 4 table

High-resolution modal analysis

Usual modal analysis techniques are based on the Fourier transform. Due to the Delta T . Delta f limitation, they perform poorly when the modal overlap mu exceeds 30%. A technique based on a high-resolution analysis algorithm and an order-detection method is presented here, with the aim of filling the gap between the low- and the high-frequency domains (30%<mu<100%). A pseudo-impulse force is applied at points of interests of a structure and the response is measured at a given point. For each pair of measurements, the impulse response of the structure is retrieved by deconvolving the pseudo-impulse force and filtering the response with the result. Following conditioning treatments, the reconstructed impulse response is analysed in different frequency-bands. In each frequency-band, the number of modes is evaluated, the frequencies and damping factors are estimated, and the complex amplitudes are finally extracted. As examples of application, the separation of the twin modes of a square plate and the partial modal analyses of aluminium plates up to a modal overlap of 70% are presented. Results measured with this new method and those calculated with an improved Rayleigh method match closely

Robust Analysis of Electromagnetic Responses of Resonant Structures using Early-time and Low-Frequency Data

The rapid increase of affordable computing resources combined with the continued development and refinement of computational electromagnetic (CEM) methods has yielded a wide range of accurate and well-verified EM modeling tools; however, improvements are required to keep pace with the current and future requirements of EM systems. One such need is the development of robust, computationally-efficient methods which provide one the means to understand complex resonant systems through the by analyzing EM responses. The characteristics of resonant systems often make the determination of a wideband response with CEM methods computationally very intensive. Also, a numerical solution may not directly provide one with the physical insight needed to identify the characteristics of a complex system that influence its EM behavior. With a clear understanding of why a system behaves as it does, one can make better-informed choices on how to modify and design structures which have the desired properties. Even with the widespread use of optimization techniques, such as the genetic algorithm, to automate the search for an optimal combination of parameters, physical insight provides a valuable perspective. It can provide guidance in the design process and also allows one to better understand why a design works, which can lead to additional ideas to pursue. Procedures to efficiently and reliably extrapolate a wideband EM response of a resonant structure in the time- and frequency-domain are presented in this dissertation. Values of the response at discrete points in early time, low frequency, and space are determined with CEM methods, and the data are extrapolated to determine a representation of the complete response in time and frequency as a sum of weighted polynomials and pole terms. The representation is accurate and compact, and it is shown to provide valuable physical insight in the resonant behavior of the structure

MiniMax Affine Estimation of Parameters of Multiple Damped Complex Exponentials

Multiple damped complex exponentials are of great practical importance as they are useful for describing many technological situations. Several estimators have been developed for the parameters of these complex exponentials. In this paper, we apply the MiniMax affine estimator to this problem in order to obtain a better performance (in terms of the mean squared error) than other unbiased estimators. Through simulations, this estimator is shown to have a reduced mean squared error, especially for the adverse case of lower signal-to-noise ratio. Additionally, a closed form expression for the MiniMax affine estimator is presented.Sociedad Argentina de Informática e Investigación Operativ

The DESAM toolbox: spectral analysis of musical audio

International audienceIn this paper is presented the DESAM Toolbox, a set of Matlab functions dedicated to the estimation of widely used spectral models for music signals. Although those models can be used in Music Information Retrieval (MIR) tasks, the core functions of the toolbox do not focus on any specific application. It is rather aimed at providing a range of state-of-the-art signal processing tools that decompose music files according to different signal models, giving rise to different ``mid-level'' representations. After motivating the need for such a toolbox, this paper offers an overview of the overall organization of the toolbox, and describes all available functionalities