Two new lapped transforms for subband/transform coding of signals are introduced: a new version of the lapped orthogonal transform (LOT), which can be efficiently computed for any transform length; and the modulated lapped transform (MLT), which is based on a modulated quadrature mirror filter (QMF) bank. The MLT can also be efficiently computed by means of a type-IC discrete sine transform (DST-IV). The LOT and the MLT are both asymptotically optimal lapped transforms for encoding AR(1) signals with a high intersample correlation coefficient. The coding gains of the LOT and the MLT of length M are higher than that of the discrete cosine transform (DCT) of the same length; they are actually closer to the coding gains obtained with a DCT of length 2M. An MLT-based adaptive transform coder (ATC) for speech signals has been simulated; the code is essentially free from frame rate noise and has a better spectral resolution than DCT-based ATC systems.