Parameter free and reliable signal denoising based on constants obtained from IMFs of white Gaussian noise

This paper proposes a denoising method based on the constants obtained from the intrinsic mode functions (IMFs) of the noise. In particular, the model based constant is calculated using the analytical form of both the energy and the mean period of the first IMF of the noise. For practical situations, the corresponding constants are obtained using the sums of logarithms of the real energies and real mean periods of the IMFs of noise. Since the corresponding constants obtained using the practical data of the high order IMFs suffer from large fluctuations, these obtained values are unreliable. To address this issue, the relative percentage errors between the corresponding constants obtained using the practical data and the calculated model based constant are computed only using the second IMF to the sixth IMF. In this case, the corresponding constants obtained using the practical data of the selected IMFs are more reliable and less fluctuated. Next, the upper bound and the lower bound of the corresponding constants obtained using the practical data of the selected IMFs are computed. As no parameter is required to be predefined in the proposed algorithm, the proposed algorithm is more reliable than the existing algorithms. Computer numerical simulation results also show that the proposed algorithm outperforms the existing algorithms.