With the development of mathematical morphology theory, the application of mathematical morphology in image processing has been very extensive, in recent years, with in-depth study of mathematical morphology and its applications in signal processing development is receiving more and more attention. As a kind of nonlinear signal processing method, its signal feature extraction is performed in time domain, compared with some other nonlinear and non-stationary signal processing method, which has no phase offset and amplitude attenuation etc. many advantages, so this method is applied to the signal processing in various industries. This paper mainly expounds the basic theory of mathematical morphology, and puts forward the method of mathematical morphology denoising pretreatment. Finally, the paper summarizes the application of mathematical morphology in speech signal processing and the combination of neural network.