Detecting a signal without aliasing suppose you are detecting a signal from a distant pulsar. the signal is, to good approximation, an infinite series of pulses arriving with a period of 5.8ms. each pulse can be approximated as a gaussian with a 1/e width of 1ms. a) write down a function for this pulse train (using a convolution). (4) b) what is the fourier transform of the pulse train? (5) c) assuming you want to sample the incoming signal. what is the minimum sampling rate (in hz) you must have in your electronics to avoid aliasing of the pulsar signal? . (a good choice of threshold might be to find the frequency such that the energy has dropped to 1 part per million of the peak energy, but you can choose as long as you explain your reasoning and calculations) (5) d) suppose you discover, to your dismay, that a rival astronomer is trying to damage your data by injecting a high frequency signal into your data that obscures your signal. what frequencies could they use to do this? (5) e) to foil the evil plan you use a low pass filter into your data acquisition system to cut out the interference signal. where do you put this filter (before or after sampling)? can you beat your rival or are there some frequencies that you can’t filter? explain your reasoning.