The complete and disjoint segmentation of a signal is defined as the Schur product of the signal with the rows of a binary matrix, whereby each column in the matrix sums to exactly one. The segmentation operation is given by,
where 
and 
is the segmented portion of 
and K is the number of segments produced. When the set 
is a complete and disjoint segmentation over the sequence of N samples it requires the following
where 
is the set of binary numbers. The perfect reconstruction binary segmentation system is illustrated in Figure 3.
Figure 3: Two split segmentation system - segmentation and summation give perfect reconstruction when 
are disjoint and complete.