1. A method for constructing a directional lapped transform for use in transforming a data signal, comprising steps for: receiving a separable lapped transform of two or more dimensions in a lifting-based format comprising both a lifting-based pre-filtering stage and a lifting-based discrete cosine transform (DCT) stage for each 1D lapped transform of the separable lapped transform; receiving a data signal of the same dimensionality as the separable lapped transform; evaluating blocks of the data signal to determine a correlation direction from a range of possible correlation directions for each block; and for at least one of the 1D lapped transforms: selectively populating lifting steps of the pre-filtering stage with data elements determined by following a path through each corresponding data block using the correlation direction determined for each data block, determining outputs of the selectively populated pre-filtering stage to produce pre-filtered data blocks corresponding to the data blocks of the data signal, and selectively populating lifting steps of the DCT stage using the outputs of the selectively populated pre-filtering stage by following a path through each pre-filtered data block using the correlation direction determined for each data block, and determining outputs of the selectively populated DCT stage to produce a directional lapped transform (DLT) of the data signal.