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.9.9 illustrates a set of frequency trajectories, including one with a missing segment due to its peak not being detected in the third frame.

Figure 9.10 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. For a more detailed description, see Appendix I.

Synthesis is performed using a bank of amplitude- and phase-modulated oscillators, as shown in Fig.9.11.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.