The GenLOT: generalized linear-phase lapped orthogonal transform

The general factorization of a linear-phase paraunitary filter bank (LPPUFB) is revisited. From this new perspective, a class of lapped orthogonal transforms with extended overlap (generalized linear-phase lapped orthogonal transforms (GenLOT’s)) is developed as a subclass of the general class of LPPUFB. In this formulation, the discrete cosine transform (DCT) is the order-1 GenLOT, the lapped orthogonal transform is the order-2 GenLOT, and so on, for any filter length that is an integer multiple of the block size. The GenLOT’s are based on the DCT and have fast implementation algorithms. The implementation of GenLOT’s is explained, including the method to process finite-length signals. The degrees of freedom in the design of GenLOT’s are described, and design examples are presented along with image compression tests.