Hyperbolic frequency modulation (HFM) is better than LFM for high radial velocities. The HFM phase is

\[
\phi_{h}(t)=\frac{\omega_{0}^{2}}{\mu_{h}} \ln \left(1+\frac{\mu_{h} \alpha t}{\omega_{0}}ight)
\]

where \(\mu_{h}\) is an HFM coefficient and \(\alpha\) is a constant. (a) Give an expression for the instantaneous frequency of an HFM pulse of duration \(\tau^{\prime}{ }_{h}\). (b) Show that HFM can be approximated by LFM. Express the LFM coefficient \(\mu_{l}\) in terms of \(\mu_{h}\) and in terms of \(B\) and \(\tau^{\prime}\).