Lapped Tight Frame Transforms

We propose a new class of equal-norm tight frames termed lapped tight frame transforms (LTFTs). These can be seen as a redundant counterpart to bases known as lapped orthogonal transforms (LOTs) introduced by Malvar and Cassereau, as well as an infinite-dimensional counterpart to harmonic tight frames (HTFs). To construct LTFTs, we seed them from LOTs and show that, in a specific case, the process preserves the equal norm. As both their basis counterpart LOTs as well as their finite-dimensional one HTFs, LTFTs possess many desirable properties, such as equal norm and efficient implementation.