Malvar wavelets with asymmetrically overlapped windows

Malvar (see ibid., vol.38, p.969-78, June 1990) wavelets (or tapped orthogonal transforms) with symmetric overlaps have been studied extensively. We consider Malvar wavelets with asymmetric overlaps in both continuous-time and discrete-time cases. We present conditions on window functions in continuous-time case so that Malvar wavelets can be constructed from different local bases. However, in discrete-time cases, we show that Malvar wavelets are impossible unless the overlaps are symmetric. Numerical examples are presented to illustrate the theory. We consider real valued signals and bases.