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

High resolution sparse estimation of exponentially decaying two-dimensional signals

In this work, we consider the problem of high-resolution estimation of the parameters detailing a two-dimensional (2-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Interpreting the estimation problem as a block (or group) sparse representation problem allows the decoupling of the 2-D data structure into a sum of outer-products of 1-D damped sinusoidal signals with unknown damping and frequency. The resulting non-zero blocks will represent each of the 1-D damped sinusoids, which may then be used as non-parametric estimates of the corresponding 1-D signals; this implies that the sought 2-D modes may be estimated using a sequence of 1-D optimization problems. The resulting sparse representation problem is solved using an iterative ADMM-based algorithm, after which the damping and frequency parameter can be estimated by a sequence of simple 1-D optimization problems

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Asymptotic Performance for Delayed Exponential Process

International audienceThe damped and delayed sinusoidal (DDS) model can be defined as the sum of sinusoids whose waveforms can be damped and delayed. This model is suitable for compactly modeling short time events. This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this correspondence, we derive exact and approximate asymptotic Cramér–Rao bounds (CRBs) for the DDS model. This analysis shows that this model has better, or at least similar, theoretical performance than the well-known exponentially damped sinusoidal (EDS) model. In particular, the performance in the DDS case is significantly improved compared to that of the EDS for closely spaced sinusoids thanks to the nonzero time delays. Consequently, we can exploit the advantageous properties of the DDS model and, in the same time, we can keep high theoretical model parameter estimation accuracy

A Two-Phase Damped-Exponential Model for Speech Synthesis

It is well known that there is room for improvement in the resultant quality of speech synthesizers in use today. This research focuses on the improvement of speech synthesis by analyzing various models for speech signals. An improvement in synthesis quality will benefit any system incorporating speech synthesis. Many synthesizers in use today use linear predictive coding (LPC) techniques and only use one set of vocal tract parameters per analysis frame or pitch period for pitch-synchronous synthesizers. This work is motivated by the two-phase analysis-synthesis model proposed by Krishnamurthy. In lieu of electroglottograph data for vocal tract model transition point determination, this work estimates this point directly from the speech signal. The work then evaluates the potential of the two-phase damped-exponential model for synthetic speech quality improvement. LPC and damped-exponential models are used for synthesis. Statistical analysis of data collected in a subjective listening test indicates a statistically significant improvement (at the 0.05 significance level) in quality using this two-phase damped-exponential model over single-phase LPC, single-phase damped-exponential and two-phase LPC for the speakers, sentences, and model orders used. This subjective test shows the potential for quality improvement of synthesized speech and supports the need for further research and testing

Estimating Sparse Signals Using Integrated Wideband Dictionaries

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance