Some limitations of the Hilbert transform (HT) for computing instantaneous characteristics of complicated mono-component signals were analyzed. As an enhancement of the HT, an algorithm named empirical AM-FM (amplitude and frequency modulation) demodulation was investigated and then improved. Firstly, the weighted smoothing phase-difference method was applied to this demodulation algorithm to increase the precision of instantaneous frequency for noisy signals. Secondly, by combining the Empirical Mode Decomposition (EMD) and the improved empirical AM-FM demodulation algorithm, a method suitable for instantaneous characteristics extraction of complicated multi-component signals was proposed. The validity of the improvements was confirmed by numerical simulations and experimental signals.