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Abstract - DSP5 |
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DSP5.1 |
Using Phase Information to Decorrelate the Filtered-X Algorithm P. Sommen, J. Garas (Eindhoven University of Technology, The Netherlands) A well known algorithm in the field of active noise control is the filtered-x algorithm. As known in literature, the convergence properties of an adaptive algorithm can be improved by decorrelating its input signal. In this paper, the decorrelation needed for the filtered-x algorithm is discussed with the help of block frequency domain adaptive filters. It is shown that decorrelation of not only the input signal but also the amplitude response of the secondary acoustic path is necessary. While the former can be done by dividing the input signal in frequency domain by an estimate of the input signal power, the latter leads to a new method for improving convergence properties without any extra computation; by using only the phase information of the secondary path to calculate the filtered-x signal. |
| DSP5.2 |
A Recursive Total Least Squares Algorithm for Deconvolution Problems P. Vandaele, M. Moonen (ESAT/SISTA K.U. Leuven, Belgium) Deconvolution problems are encountered in signal processing applications where an unknown input signal can only be observed after propagation through one or more noise corrupted FIR channels. The first step in recovering the input usually entails an estimation of the FIR channels through training based or blind algorithms. The 'standard' procedure then uses least squares estimation to recover the input. A recursive implementation with constant computational cost is based on the Kalman filter. In this paper we focus on a total least squares based approach, which is more appropriate if errors are expected both on the output samples and the estimates of the FIR channels. We will develop a recursive total least squares algorithm (RTLS) which closely approximates the performance of the non-recursive TLS algorithm and this at a much lower computational cost. |
| DSP5.3 |
Computationally Efficient Algorithms for Third Order Adaptive Volterra Filters X. Li, W. Jenkins (University of Illinois - Coordinated Science Lab, USA); C. Therrien (Naval Postgraduate School, USA) The input autocorrelation matrix for a third order (cubic) Volterra adaptive filter for general colored Gaussian input processes is analyzed to determine how to best formulate a computationally efficient fast adaptive algorithm. When the input signal samples are ordered properly within the input data vector, the autocorrelation matrix of the cubic filter inherits a block diagonal structure, with some of the sub-blocks also having diagonal structure. A computationally efficient adaptive algorithm is presented that takes advantage of the sparsity and unique structure of the correlation matrix that results from this formulation. |
| DSP5.4 |
Numerical Stability Issues of the Conventional Recursive Least Squares Algorithm A. Liavas, P. Regalia (Institut National des Telecommunications, France) The continuous use of adaptive algorithms is strongly dependent on their behavior in finite-precision environments. We study the nonlinear round-off error accumulation system of the conventional RLS algorithm and we derive bounds for the relative precision of the computations which guarantee the numerical stability of the finite-precision implementation of the algorithm. The bounds depend on the conditioning of the problem and the exponential forgetting factor. Simulations agree with our theoretical results. |
| DSP5.5 |
A Combined FDAF/WSAF Algorithm for Stereophonic Acoustic Echo Cancellation F. Alberge, P. Duhamel, Y. Grenier (Ecole Nationale Superieure des Telecommunications, France) Adaptive acoustic echo cancellation in stereophonic teleconferencing is a very demanding application. Characteristics are : very large number of coefficients, non-stationary input (speech), (slowly) time-varying systems to be identified, plus the specific property that both stereo signals are intrinsically very correlated. Basic versions of stochastic gradient algorithms have difficulties to meet these requirements. We show that, in a multi-channel framework, only a combination of techniques can result in an algorithm which convergence is governed by a quasi-diagonal matrix. Simulations with data recorded in a conference room demonstrate the improvement in convergence of our algorithm compared to the LMS. |
| DSP5.6 |
Bounding the Performance of the LMS Estimator for Cases where Performance Exceeds that of the Finite Wiener Filter K. Quirk, J. Zeidler, L. Milstein (University of California, San Diego, USA) The least-mean-square (LMS) estimator is a nonlinear estimator with information dependencies spanning the entire set of data fed into it. The traditional analysis techniques which are used to model this estimator obscure this, restricting the estimator to the finite set of data sufficient to span the length of its filter. The finite Wiener filter is thus often considered a bound on the performance of the LMS estimator. Several papers have reported the performance of the LMS filter exceeding that of the finite Wiener filter. In this paper, we will demonstrate a bound on the LMS estimator, which does not exclude the contributions from data outside its filter length, and which demonstrates the ability of the LMS estimator to outperform the finite Wiener filter in certain cases. |
| DSP5.7 |
Stochastic Analysis of Gradient Adaptive Identification of Nonlinear Systems with Memory N. Bershad (University of California, Irvine, USA); P. Celka, J. Vesin (Signal Proc. Lab. EPFL, Switzerland) This paper analyzes the statistical behavior of a sequential gradient search adaptive algorithm for identifying an unknown nonlinear system comprised of a discrete-time linear system H followed by a zero-memory nonlinearity g(.). The LMS algorithm first estimates H. The weights are then frozen. Recursions are derived for the mean and fluctuation behavior of LMS which agree with Monte Carlo simulations. When the nonlinearity is modelled by a scaled error function, the second part of the gradient scheme is shown to correctly learn the scale factor and the error function scale factor. Mean recursions for the scale factors show good agreement with Monte Carlo simulations. |
| DSP5.8 |
An Unbiased Equation-Error-Based Adaptive IIR Filtering Algorithm S. Sankaran, L. Beex (Virginia Tech, USA) We modify the off-line system identification procedure proposed by Regalia into an adaptive IIR filtering algorithm based on the stochastic gradient method. The proposed algorithm aims to minimize equation error, recursively, under a unit-norm constraint on the characteristic polynomial instead of the usual monic constraint. The unit-norm constraint eliminates the bias associated with equation error based estimates, when the additive measurement noise is white. The unit-norm constraint is enforced by adapting the parameters of the characteristic polynomial in (hyper)spherical coordinates. Simulation results indicate that the proposed algorithm provides estimates that are unbiased and that it is a computationally efficient alternative, for the same performance, to FIR adaptive filters. |
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