This letter extends our recently introduced method which was designed to estimate instantaneous frequency and chirp rate of linearly modulated signals. Indeed, we derive several new estimators related to our previous ones which provide in the timefrequency plane all the signal parameters of the investigated model: amplitude, frequency, and their local modulations (AM/FM). Our estimators are first introduced and compared in terms of statistical efficiency with theoretical bounds and with other state-of-the-art estimators.Then, they are used to improve spectral analysis applied to audio sinusoidal modeling. Finally, they lead to a new source separation technique based on coherent amplitude and frequency modulation that is evaluated on real-world music signals.