Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

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.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 7.3: Sinusoidal frequency trajectories.
\includegraphics[width=\textwidth ]{eps/tracks}

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.


\begin{psfrags}
% latex2html id marker 20393\psfrag{s} []{\normalsize$s(t)$}...
...am
of a sinusoidal-modeling \emph{analysis} system.}
\end{figure}
\end{psfrags}

Synthesis is performed using a bank of amplitude- and phase-modulated oscillators, as shown in Fig.7.5.


\begin{psfrags}
% latex2html id marker 20403\psfrag{T} []{ \normalsize$ \Theta...
...ng \emph{synthesis} system (phase-preserving case).}
\end{figure}
\end{psfrags}


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]

``Spectral Audio Signal Processing'', by Julius O. Smith III, (March 2007 Draft).
Copyright © 2008-05-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [About the Automatic Links]