24. (b) Close-pairs dots at entry number 1 and delays 1 and 2 means |x1 - x2| < filter and |x1 - x3| < filter. There need not be a close-pairs dot at entry number 2 and delay 1, because that would require |x2 - x3| < filter, not a necessary consequence of the dots in the first column. For example, if x2 = x1 - (2/3)*filter and x3 = x1 + (2/3)*filter, then |x1 - x2| < filter, |x1 - x3| < filter, and yet |x2 - x3| = (4/3)*filter.

Return to Exercises