NUMBER THEORETIC SOLUTIONS TO INTERCEPT TIME PROBLEMS/

We consider a number of problems concerning the overlaps or coincidenc es of two periodic pulse trains. We show that the first intercept time of two pulse trains started in phase is a homogeneous Diophantine app roximation problem which can be solved using the convergents of the si mple continued fraction (s.c.f.) expansion of the ratio of their pulse repetition intervals (PRI's). We find that the intercept time for arb itrary starting phases is an inhomogeneous Diophantine approximation p roblem which can be solved in a similar manner, We give a recurrence e quation to determine the times at which subsequent coincidences occur, We then demonstrate how the convergents of the s.c.f. expansion can b e used to determine the probability of intercept of the two pulse trai ns after a specified time when one or both of the initial phases are r andom, Finally, we discuss how the probability of intercept varies as a function of the PRI's and its dependence on the Farey points.