Performance of Wavelet Transform and Empirical Mode Decomposition in Extracting Signals Embedded in Noise

Time-frequency transformations have gained increasing attention for the characterization of nonstationary signals in a broad spectrum of science and engineering applications. This study evaluates the performance of two popular transformations, the continuous wavelet transform and empirical mode decomposition with Hilbert transform $(\mathrm{EMD}+\mathrm{HT})$ , in estimating instantaneous frequency (IF) in the presence of noise. The findings demonstrate that under these conditions wavelets seeking harmonic similitude at various scales produce lower variance IF estimates than $\mathrm{EMD}+\mathrm{HT}$ . The shortcomings of the latter approach are attributed to its empirical, envelope-dependent nature, leading to bases that are themselves derived from noise.