Additive Synthesis Analysis

In order to reproduce a given signal, we must first analyze it to determine the amplitude and frequency trajectories for each sinusoidal component. We do not need phase information ($\phi_i$ in (10.18)) during steady-state segments, since phase is normally not perceived in steady state tones [293,211]. However, we do need phase information for analysis frames containing an attack transient, or any other abrupt change in the signal. The phase of the sinusoidal peaks controls the position of time-domain features of the waveform within the analysis frame.