Abstract: Aiming at the problems of slow convergence speed and large steady-state error of the minimum mean square error algorithm in speech noise reduction, we proposed a variable-step minimum mean square error algorithm based on wavelet threshold. Firstly, the time-frequency analysis of the speech signal was carried out by using the wavelet soft threshold algorithm, the wavelet coefficients of noise were eliminated, and the noise reduction accuracy was improved. Secondly, on the basis of the minimum mean square error algorithm, we proposed  a new variable step size minimum mean square error algorithm to further denoise the transformed speech signal by establishing the nonlinear function relationship between the step size factor and the error signal. 
The experimental results show that compared with other single denoising algorithms, this algorithm has a great  improvement in signal-to-noise ratio and mean square error.

Key words: signal filtering; , minimum mean square error algorithm； wavelet threshold; , signal processing