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It has been established in the literature that a time-limited linear time invariant (LTI) system can be uniquely identified from its cyclostationary output autocorrelation when the input is a sequence of equispaced Dirac delta functions with independent identically distributed (i.i.d.) random amplitudes. The authors show that this is, however, not true for a band-limited system. A necessary and sufficient condition for a band-limited system to be uniquely identified from its cyclostationary output autocorrelation is given