This paper addresses the problem of speech enhancement and acoustic noise reduction by adaptive filtering algorithms. Recently, we have proposed a new Forward blind source separation algorithm that enhances very noisy speech signals with a subband approach. In this paper, we propose a new variable subband step-sizes algorithm that allows improving the previous algorithm behaviour when the number of subband is selected high. This new proposed algorithm is based on recursive formulas to compute the new variable step-sizes of the cross-coupling filters by using the decorrelation criterion between the estimated sub-signals at each subband output. This new algorithm has shown an important improvement in the steady state and the mean square error values. Along this paper, we present the obtained simulation results by the proposed algorithm that confirm its superiority in comparison with its original version that employs fixed step-sizes of the cross-coupling adaptive filters and with another fullband algorithm. decimation factor interpolation factor index varied between 0 and N-1 decimated time index analysis and synthesis filters lengths real and adaptive filters lengths delay index subbands number time index small positive constant small positive constant small positive constant fast transversal filter fast Newton transversal filter two-channel fullband backward two-channel subband forward acoustic echo cancellation acoustic noise reduction affine projection algorithm blind source separation Forward blind source separation Backward blind source separation fixed step-size impulse response(s) least mean squares normalized LMS two-channel Forward NLMS recursive least square subband adaptive filtering symmetric adaptive decorrelating system mismatch signal-to-noise ratio segmental signal-to-noise ratio cepstral distance mean square error voice activity detector variable-step-size decibel voice activity detector singular value decomposition discrete wavelet transform packet wavelet transform expectation operator smoothed parameter original speech signal noise cross-coupling IRs noisy speech signals Kronecker impulse analysis filters synthesis filters noisy speech sub-signals estimated speech sub-signals estimated noise sub-signals symmetric adaptive filters enhanced speech signal estimated noise Lagrange multipliers sampling frequency fixed step-sizes minimal step-sizes maximal step-sizes controlled step-sizes cross-correlation factors functions deviation vectors 
Improved subband-forward algorithm for acoustic noise reduction and speech quality enhancement