Suppose the ambiguity function of some waveform x(t) of duration ζ = 1 millisecond is given by
(NOTE: this is not a possible AF because it is not time-limited to ±ζ seconds duration in the delay coordinate, but it will do for this problem.) Suppose there are two targets in our line of sight, one at R = 10 km and one at R = 10.1 km. Also assume that both have the same RCS, and ignore the effect of the small range difference on the received echo power. The radar and the first target are stationary. The second target is traveling towards the radar at 100 m/s. The radar is operating at 1 GHz. What is the Doppler shift of the echo from the second target, in Hz? If the matched filter output is sampled at a time delay corresponding to the range to the first target (= 2*(10 km)/c = 66.67 μs), the sample will contain contributions from both the first and second targets. Use A(t,F_{D}) to determine the amplitude of the contribution from the second target to the sample timed to correspond to the first target. Express your answer in dB.