By cascading the filtering and segmentation, the segmentation operator can be incorporated into the filter bank in two ways: (1) segmentation before analysis filtering, and (2) segmentation after analysis filtering. In practice, these are not equivalent because the filtering requires a border extension of the signal. Typically, with a rule-based border extension such as periodic extension, the added border data differ in the two cases. However, with the segmentations included in the filter bank, perfect reconstruction can still be maintained in both cases.
)
Applying the complete set of segmentation functions 
to each of the outputs of the analysis section of the filter bank produces the segmentation of the subbands. Each of the subband segments, 
is obtained from
Since the segmentation operation is invertible, the subbands can be reconstructed by summing the segments of each subband. Therefore, the perfect reconstruction property of the filter bank is maintained when the subbands are reconstructed before synthesis filtering.
)Applying the segmentation before subband decomposition creates multiple filter bank paths, one for each segment. Since each of the two channel filtering maintains perfect reconstruction of the segment, the overall system is perfect reconstruction.