Shazia Javed

A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.

Adaptive total least squares based speech prediction

In this paper, an instantaneous total error based adaptive linear predictor is presented for linear predictive coding (LPC) of speech signals. In LPC, the speech signal is predicted by a linear combination of delayed input signals that are contaminated by noise. For this reason, total least mean squares (T-LMS) algorithm is used to decode the noisy input signals and to predict a speech signal. A compressed speech prediction is done when the mean squares total error is minimized, showing the efficiency of T-LMS based LPC model. Experimental results are recorded for different values of signal to noise ratio (SNR) of the input signals, and a comparative study is presented with instantaneous error squares based adaptive filter. These results show the preference of proposed predictor over the other.

Performance study of LMS based adaptive algorithms for unknown system identification

Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.

Noise Cancelation From ECG Signals Using Householder-RLS Adaptive Filter

In this paper an adaptive recursive least squares filter is used for removal of artifacts from clinical ECG signals. The householder RLS (HRLS) algorithm is an efficient algorithm which recursively updates an arbitrary square-root of the input data correlation matrix and naturally provides the LS weight vector. A data dependent householder matrix is applied for such an update. In this paper an adaptive noise canceler (ANC) is designed for ECG denoising using HRLS algorithm. The promising characteristic of proposed ANC is its flexibility in choosing the reference signals, because it has a trade off between the correlation properties of the noise and the reference signals. Simulation results show the efficiency of RLS based algorithms in ECG denoising.

A recursive block incomplete factorization preconditioner for adaptive filtering problem

In this paper a recursive incomplete factorization preconditioner for the iterative solvers of adaptive filtering problem is proposed. The preconditioner is able to reduce the eigenvalue spread of the input signals. The technique involves QR factorization of a toeplitz block sub matrix of the input data matrix. Incomplete factorization is realized by block-diagonalization of the upper triangular factor. The preconditioner obtained by update of the incomplete upper triangular factor, with no fill-ins, has low computational cost as compared with complete factor update. With appropriate choice of the number of diagonal blocks, the computational cost of the resulting preconditioner can be reduced significantly. Simulations results show noticeable decrease in the spectral condition number of the autocorrelation matrix by the application of resulting preconditioner.

An incomplete factorization preconditioner for adaptive filtering

A method for deriving an incomplete QR factorization preconditioner for adaptive filtering is proposed. The method combines a recursive inverse QR factorization with a dropping strategy. Inverse QR factorization is more efficient compared to conventional factorization methods in that it avoids direct computation of the inverse. By realizing the factorization using a series of Givens rotation, a direct calculation of the inverse Cholesky factor is possible through the use of matrix inversion lemma and some algebraic manipulation of the Givens parameters. A dropping strategy is designed to create sparseness in the inverse Cholesky factor therefore minimizing the computational complexity of the resulting algorithm. Simulation shows that the incomplete inverse Cholesky factor derived in this paper is able to reduce the spectral condition number of the autocorrelation matrix of the problem.