Passive Acoustic Mapping (PAM) enables real-time monitoring of ultrasound therapies by beamforming acoustic emissions emanating from the ultrasound focus. Reconstruction of the narrowband or broadband acoustic emissions component enables mapping of different physical phenomena, with narrowband emissions arising from non-linear propagation and scattering, non-inertial cavitation or tissue boiling, and broadband (generally, of significantly lower amplitude) indicating inertial cavitation. Currently, accurate classification of the received signals based on pre-defined frequency-domain comb filters cannot be guaranteed because varying levels of leakage occur as a function of signal amplitude and the choice of windowing function. This work presents a time-domain parametric model aimed at enabling accurate estimation of the amplitude of time-varying narrowband components in the presence of broadband signals. Conversely, the method makes it possible to recover a weak broadband signal in the presence of a dominant harmonic or other narrowband component. Compared to conventional comb filtering, the proposed sum-of-harmonics method enables PAM of cavitation sources that better reflect their physical location and extent.