Instantaneous Parameters of Signals and Orthogonal Bases of Wavelets
Shi‐Xiong Li, Ji-Wen WANG · Chinese Journal of Geophysics · 2000
Abstract If a real signal can be written in the form u(t) = a(t) cos θ(t), we call a(t), θ(t) and graphic the instantaneous amplitude, phase and frequency of u(t), respectively. In many practical fields, the extraction of such instantaneous parameters as instantaneous amplitude, phase and frequency, is quite important. However, the existing methods for calculation of instantaneous parameters have some defects. In this paper, we construct a kind of wavelet, which has compact support in the frequency domain, and the Fourier transform of the wavelet has analytic expression. Using these wavelets, we obtain a fast, local and de‐noising algorithm for calculation of instantaneous parameters of signal. Theoretical analysis and numerical simulations show that our method is practical and efficient. It is believed that this method can meet the needs of many practical fields.