We apply discrete Fourier transforms to musical tempo. Then we perform pitch saliency-based melody extraction for each frame. Secondly, we use the finite element differential mathematical model for speech tracking with non-fixed parameters. In this paper, the masking threshold of each edge of the speech signal is dynamically determined by introducing a Bayesian tangent shape model. The simulation results show that the finite element differential mathematical model can remove the noise in the speech signal to a certain extent. In the environment of a low signal-to-noise ratio, the advantages of this algorithm over other spectral subtraction methods are more significant.