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.7.3 illustrates a set of frequency trajectories, including one with a missing segment due to its peak not being detected in the third frame.
Figure 7.4 depicts the general analysis system. ``Non-coherent'' sinusoidal parameter estimation from magnitude spectrum (peak amplitude, center-frequency, and sometimes phase). Quadratic interpolation used to accurately find spectral magnitude peaks. The Short Time (fast) Fourier Transform (STFT) is used for analysis.
Synthesis is performed using a bank of amplitude- and phase-modulated oscillators, as shown in Fig.7.5.