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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 [292,210]. 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.



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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
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Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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