In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.

In this letter, a design method of linear-phase paraunitary filter banks is proposed for an odd number of channels. In the proposed method, a non-linear unconstrained optimization process is assumed to be applied to a lattice structure which makes the starting guess of design parameters simple. In order to avoid insignificant local minimum solutions, a recursive initialization procedure is proposed. The significance of our proposed method is verified by some design examples.

In this work, a new structure of M-channel linear-phase paraunitary filter banks is proposed, where M is even. Our proposed structure can be regarded as a modification of the conventional generalized linear-phase lapped orthogonal transforms (GenLOT) based on the discrete cosine transform (DCT). The main purpose of this work is to overcome the limitation of the conventional DCT-based GenLOT, and improve the performance of the fast implementation. It is shown that our proposed fast GenLOT is superior to that of the conventional technique in terms of the coding gain. This work also provides a recursive initialization design procedure so as to avoid insignificant local-minimum solutions in the non-linear optimization processes. In order to verify the significance of our proposed method, several design examples are given. Furthermore, it is shown that the fast implementation can be used to construct M-band linear-phase orthonormal wavelets with regularity.