An efficient lapped transform is realized using pre- and post-filters (or reversible overlap operators) that are structured of unit determinant component matrices. The pre-and post-filters are realized as a succession of planar rotational transforms and unit determinant planar scaling transforms. The planar scaling transforms can be implemented using planar shears or lifting steps. Further, the planar rotations and planar shears have an implementation as reversible/lossless operations, giving as a result, a reversible overlap operator.