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Tracking Sinusoidal Peaks in a Sequence of FFTs

The preceding discussion focused on estimating sinusoidal peaks in a single frame of data. For estimating sinusoidal parameter trajectories through time, it is necessary to associate peaks from one frame to the next. For example, Fig.10.9 illustrates a set of frequency trajectories, including one with a missing segment due to its peak not being detected in the third frame.

Figure 10.9: Sinusoidal frequency trajectories.

Figure 10.10 depicts a basic analysis system for tracking spectral peaks in the STFT [271]. The system tracks peak amplitude, center-frequency, and sometimes phase. Quadratic interpolation is used to accurately find spectral magnitude peaks (§5.7). For further analysis details, see Appendix H. Synthesis is performed using a bank of amplitude- and phase-modulated oscillators, as shown in Fig.10.7. Alternatively, the sinusoids are synthesized using an inverse FFT [239,94,139].

% latex2html id marker 28143\psfrag{s} []{\Large$s(t)$}\psfrag{tan} []{\Large$\tan^{-1}$}\begin{figure}[htbp]
\caption{Block diagram
of a sinusoidal-modeling \emph{analysis} system
(from \cite{SerraT}).}

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University