Pedro D. Doñate

Factorized All-Pass Based IIR Adaptive Notch Filters

This paper introduces a new family of infinite impulse response adaptive notch filters that forms multiple notches using a second-order factorization of an all-pass transfer function. The new orthogonal realization is amenable for adaptive filtering to obtain the unknown frequencies of interest. Two new adaptive filtering algorithms are presented that can achieve fast convergence at low computational cost. Local convergence analysis for the new algorithms is performed, and a detailed discussion of their properties is provided. The new all-pass based notch realization introduces a different compromise between bias and signal-to-noise ratio (SNR) when compared with realizations previously reported in the literature. Specifically, it achieves lower bias than other approaches at low SNR. This property is particularly attractive for the estimation and tracking of multiple sinusoids. Furthermore, the bias can be made arbitrarily small or can be accurately estimated and compensated for. Extensive computer simulations are provided to illustrate the performance of the proposed adaptive notch filters in terms of bias, speed of convergence, and tracking capability.

Analysis of static and dynamic bifurcations from a feedback systems perspective

In this paper, several static and dynamic bifurcation conditions for nonlinear dynamical systems are obtained from a feedback systems approach. The static bifurcations are related to the multiplicity of the steady-state solutions, while the dynamic bifurcations are connected to the appearance of periodic solutions from the equilibrium curve under the Hopf bifurcation mechanism. Examples containing elementary bifurcations are presented with an input-output description of the system, also known as the frequency-domain approach, involving applications of the generalized Nyquist stability criterion (GNSC) and harmonic balance techniques. Simple degenerate Hopf bifurcations - in a hand calculation example as well as in a more elaborated numerical problem-are also shown. The approach has a feedback characteristic flavour as compared to the classical results obtained in the traditional time-domain setting. Analysing Hopf bifurcations from such a feedback systems perspective is deemed to be a preliminary step to ...

On reduced complexity IIR adaptive filters

Reduced complexity IIR adaptive filters, like Laguerre adaptive filters with pole updating are being considered as an alternative to full adaptive IIR schemes. On the other hand, low complexity realizations exist that allow a better compromise between filter-order and modeling performance. We discuss, in this work, characteristics and properties of a reduced complexity IIR orthogonal realization that improve on those of the Laguerre and sub-optimal IIR counterparts. After reviewing the Laguerre and sub-optimal adaptive filters with pole updating, we introduce a reduced complexity IIR adaptive filter based on the Steiglitz-McBride method. The particular realization proposed is based on a generalized orthonormal family of functions. The Steitglitz-McBride method is discussed mainly because it can avoid the local minima problem related to direct mean squared output error minimization. Computer simulations are given to illustrate the good performance of the proposed adaptive IIR filter with respect to computational complexity and modeling capability if compared with its Laguerre counterpart.

Modeling and decision feedback equalization of uncertain channels

In this paper a methodology for uncertain linear communication channel modeling is evaluated. The resulting extended model is then used for the design of decision feedback equalizers (DFE). Considering an initial nonparametric description of the channel by experimental data, a model for nominal channel and uncertainty is developed by means of orthonormal function series expansion. The procedure shows good model to data fitting. Using this model a partially adaptive decision feedback equalizer is then designed. The fixed front end or precursor filter is designed as an optimal robust linear deconvolution filter. The postcursor filter is designed with a fixed denominator to optimally cancel residual past symbol interference and the numerator is treated as an adaptive FIR filter with a small number of taps. Simulation results show extended equalizer flexibility at low additional computational cost for the proposed DFE design.

Early Introduction of Robust Control Concepts: Hands-On Experience and CAD

This paper presents an educational experience in an initial course in feedback control. The purpose is to introduce the concepts of robust design not included in the regular curriculum. The problem of designing a controller for a simple mechanical system without knowing the true value of the parameters is proposed in a laboratory class. The task is performed on the real system with the aid of Computer-Aided Design freeware. The combination of practice and software tools encourages the development of autonomous learning and favours the apprehension of the concepts of uncertainty and robustness. A perception survey shows promising results indicating that the strategy of learning by doing is very well accepted by the students.

Robust orthogonal adaptive deconvolution

This article presents an adaptive deconvolution processor with an orthogonal structure. The processor is designed to be robust to small parametric uncertainties in the model. Additionally, larger changes in the system dynamics can be tracked by adapting the coefficients that linearly combine the fixed robust basis. Performance comparisons are included between the nominal, FIR and the proposed design.

Factorized all-pass IIR adaptive notch filters

A new family of IIR adaptive notch filters is presented. The family is based on a second-order factorization of the all-pass transfer function that forms the multiple notch filter. These realizations represent an extension of a previous ad-hoc scheme for adaptive notch filtering that avoids a high-order polynomial root finding in order to obtain the unknown frequencies of interest. An interesting aspect related to these novel algorithms is the fact that they introduce a different compromise between bias and SNR if compared with previous realizations available in the literature. Specifically, lower bias than in other approaches for low SNR can be achieved using the new realizations. This property is particularly attractive for multiple sinusoids estimation and tracking. In addition to the algorithm presentation, a discussion of the different properties and characteristics (stationary points, convergence) is included. Also, computer simulations are presented to illustrate the expected performance of the proposed adaptive filters.

A robust orthogonal adaptive approach to SISO deconvolution

This paper formulates in a common framework some results from the fields of robust filtering, function approximation with orthogonal basis, and adaptive filtering, and applies them for the design of a general deconvolution processor for SISO systems. The processor is designed to be robust to small parametric uncertainties in the system model, with a partially adaptive orthogonal structure. A simple gradient type of adaptive algorithm is applied to update the coefficients that linearly combine the fixed robust basis functions used to represent the deconvolver. The advantages of the design are inherited from the mentioned fields: low sensitivity to parameter uncertainty in the system model, good numerical and structural behaviour, and the capability of tracking changes in the systems dynamics. The linear equalization of a simple ADSL channel model is presented as an example including comparisons between the optimal nominal, adaptive FIR, and the proposed design.