Stochastic Analysis of the LMS Algorithm for System Identification with Subspace Inputs

This paper studies the behavior of the low rank LMS adaptive algorithm for the general case in which the input transformation may not capture the exact input subspace. It is shown that the Independence Theory and the independent additive noise model are not applicable to this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to the Independence Theory model). The new theory is applied to a network echo cancellation scheme which uses partial-Haar input vector transformations. Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the Independence Theory based model available in the literature

The Application of Blind Source Separation to Feature Decorrelation and Normalizations

We apply a Blind Source Separation BSS algorithm to the decorrelation of Mel-warped cepstra. The observed cepstra are modeled as a convolutive mixture of independent source cepstra. The algorithm aims to minimize a cross-spectral correlation at different lags to reconstruct the source cepstra. Results show that using "independent" cepstra as features leads to a reduction in the WER.Finally, we present three different enhancements to the BSS algorithm. We also present some results of these deviations of the original algorithm

A new general expression for 2-channel FIR paraunitary filterbanks

This paper provides a new explicit expression for all real FIR paraunitary filters. From this we derive a new procedure for the design of the L components of any 2-channel FIR orthogonal L-tap filter. The input of this algorithm is any set of L/2 free parameters. Moreover, our procedure provides a parameterization of all orthogonal filters directly, with no need for iterations. For the special case of low-pass paraunitary filters, we obtain a fast new design algorithm. Simplified expressions for the frequency response of paraunitary filters are also provided. In addition to these improvements, our results also yield exact solutions of a particular set of Bézout polynomial equations

Hankel-norm approximation of FIR filters: a descriptor-systems based approach

We propose a new method for approximating a matrix finite impulse response (FIR) filter by an infinite impulse response (IIR) filter of lower McMillan degree. This is based on a technique for approximating discrete-time descriptor systems and requires only standard linear algebraic routines, while avoiding altogether the solution of two matrix Lyapunov equations which is computationally expensive. Both the optimal and the suboptimal cases are addressed using a unified treatment. A detailed solution is developed in state-space or polynomial form, using only the Markov parameters of the FIR filter which is approximated. The method is finally applied to the design of scalar IIR filters with specified magnitude frequency-response tolerances and approximately linear-phase characteristics. A priori bounds on the magnitude and phase errors are obtained which may be used to select the reduced-order IIR filter order which satisfies the specified design tolerances. The effectiveness of the method is illustrated with a numerical example. Additional applications of the method are also briefly discussed

MIMO decision feedback equalization from an H∞ perspective

We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H∞ estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H∞ optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H∞ optimal. The H∞ approach also suggests a method for dealing with errors in previous decisions