Robust estimation of instantaneous phase using a time-frequency adaptive filter

The instantaneous phase estimated by the Hilbert transform (HT) is susceptible to noise; we propose a robust approach for the estimation of instantaneous phase in noisy situations. The main procedure of the proposed method is applying an adaptive filter in time-frequency domain and calculating the analytic signal. By supposing that one frequency component with higher amplitude has higher signal-to-noise ratio, a zero-phase adaptive filter, which is constructed by using the time-frequency amplitude spectrum, enhances the frequency components with higher amplitudes and suppresses those with lower amplitudes. The estimation of instantaneous frequency, which is defined as the derivative of instantaneous phase, is also improved by the proposed robust instantaneous phase estimation method. Synthetic and field data sets are used to demonstrate the performance of the proposed method for the estimation of instantaneous phase and frequency, compared by the HT and short-time-Fourier-transform methods.