BIORTHOGONAL AND NONUNIFORM LAPPED TRANSFORMS FOR TRANSFORM CODING WITH REDUCED BLOCKING AND RINGING ARTIFACTS

New lapped transforms are introduced, The lapped biorthogonal transfor m (LET) and hierarchical lapped biorthogonal transform (HLBT) are appr opriate for image coding, and the modulated lapped biorthogonal transf orm (MLBT) and nonuniform modulated lapped biorthogonal transform (NML BT) are appropriate for audio coding, The HLBT has a significantly low er computational complexity than the lapped orthogonal transform (LOT) , essentially no blocking artifacts, and fewer ringing artifacts than the commonly used discrete cosine transform (DCT), The LET and HLBT ha ve transform coding gains that are typically between 0.5 and 1.2 dB hi gher than that of the DCT, Image coding examples using JPEG and embedd ed zerotree coders demonstrate the better performance of the LET and H LBT. The NMLBT has fewer ringing artifacts and better reproduction of transient sounds than the MLT, as shown in audio coding examples, Fast algorithms for both the HLBT and the NMLBT are presented.