Chirplet Frequency-Rate Estimation

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 $ w(n)$ .

  • Let $ [c_m]$ and $ [c_p]$ denote weighted averages of the measured curvatures $ c_m(k)$ and $ c_p(k)$ 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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