A new pre-whitening transform domain LMS algorithm and its application to speech denoising

• A novel pre-whitening transform domain LMS algorithm is proposed.
• This pre-whitening is introduced before applying the transform to reinforce its decorrelation using a simple finite impulse response decorrelation filter of order one.
• In adaptive speech denoising, the proposed algorithm outperforms the conventional algorithms for different transforms in terms of the computational complexity, mean square error convergence speed, reached steady state level, residual noise in the denoised signal, steady state excess mean square error, misadjustment and output SNR.

In this paper, we propose a new pre-whitening transform domain LMS algorithm. The main idea is to introduce a pre-whitening using a simple finite impulse response decorrelation filter of order one before applying the transform to reinforce its decorrelation. The resulting algorithm has the advantage of using any transform even with low decorrelation. This advantage can be exploited to consider transforms having lower computational and structural complexities than those of the classical transforms. For this purpose, we also investigate the use of other transforms, namely the parametric Fourier and Hartley transforms. This investigation is accomplished by studying the eigenvalue spreads obtained by a given parametric transform and then finding the value of the parameter corresponding to the minimum eigenvalue spread, which is equivalent to the best mean square error (MSE) convergence behavior. This approach provides new attractive transforms for the proposed algorithm. Moreover, we consider the adaptive speech denoising as an application to evaluate the performance of the proposed algorithm. The comparisons between the proposed and conventional algorithms for different transforms are performed in terms of the computational complexity, MSE convergence speed, reached steady state level, residual noise in the denoised signal, steady state excess MSE, misadjustment and output SNR.