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