(a) Write an expression for the ambiguity function of an LFM signal with bandwidth \(B=10 \mathrm{MHZ}\), pulse width \(\tau^{\prime}=1 \mu \mathrm{s}\), and wavelength \(\lambda=1 \mathrm{~cm}\). 

(b) Plot the zero Doppler cut of the ambiguity function. 

(c) Assume a target moving toward the radar with radial velocity \(v_{r}=100 \mathrm{~m} / \mathrm{s}\). What is the Doppler shift associated with this target? 

(d) Plot the ambiguity function for the Doppler cut in part (c). 

(e) Assume that three pulses are transmitted with PRF \(f_{r}=2000 \mathrm{~Hz}\). Repeat part (b).