Analysis of the Approximation

To analyze the accuracy of the approximation, and to compare it with other methods, a set of one-dimensional vectors was generated for speech signal by Monte-Carlo simulation. These speech vectors were corrupted by adding noise at different SNR. Noise vectors were also generated by Monte-Carlo simulation.

The mean of corrupted speech estimated by different methods has been plotted in Figure 2. The result shows that Lagrange polynomial approximation gives almost the same result as given by Monte-Carlo simulation, and thus outperforms VTS-1 and log-max approximations.

図 2: Estimated mean of corrupted speech: by Monte-Carlo simulation, Log-max approximation, Vector Taylor Series-1, and Lagrange Polynomial Approximation (LPA) for $\mu _n=10$, $\sigma _n^2=0.1$, $\sigma _x^2=6$ and $\mu _x$ varying from 0 to 20.