Hyperbolic frequency modulation (HFM) is better than LFM for high radial velocities. The HFM phase is Wh(t) 2 + th Han 000 where , is an HFM coefficient and a is a constant.

(a) Give an expression for the instantaneous frequency of a HFM pulse of duration t'h.

(b) Show that HFM can be approximated by LFM. Express the LFM coefficient u, in terms of , and in terms of B and t'.