I am trying to understand the limits of down sampling on a signal, i.e. how far can I go without loss of information or overlapping. It says in the solution manual of the Oppenhiem and Schafer book (on a question where down sampling is 2) that
"There is no loss of information if X(e^(jw/2) ) and X( e^(j(w/2) - pi) ) do not overlap."
Does this mean that my original signal is periodic and when I down sample means that my frequency response X(e^jw) becomes X(e^(jw/2) ) ?