Chirplet Frequency-Rate Estimation

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The chirp rate $\beta$ may be estimated from the relation $\beta = \alpha c_m/c_p$ as follows:

Let ${\hat \alpha}$ denote the measured (or known) curvature at the midpoint of the analysis window .
Let and denote weighted averages of the measured curvatures and along the log-magnitude and phase of a spectral peak, respectively.
Then the chirp-rate $\beta$ estimate may be estimated from the spectral peak by

$\displaystyle \zbox {{\hat \beta}\isdefs {\hat \alpha}\frac{[c_p]}{[c_m]}}$

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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.

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