This paper discusses a design technique for multidimensional (M-D) multirate filters which cause no checkerboard distortion. In the first part of this paper, a necessary and sufficient condition for M-D multirate filters to be checkerboard-distortion-free is derived in the frequency domain. Then, in the second part, this result is applied to a scanning line conversion system for television signals. To confirm the effectiveness of the derived condition, band-limiting filters with and without considering the condition are designed, and the results by these filters are compared. A reducibility of the number of delay elements in such a system is also considered to derive efficient implementation.

The checkerboard effect is caused by the periodic time-variant property of multirate filters which consist of up-samplers and digital filters. Although the conditions for some one-dimensional (1D) multirate systems to avoid the checkerboard effect have been shown, the conditions for Multidimensional (MD) multirate systems have not been considered. In this paper, some theorems about the conditions for MD multirate filters without checkerboard effect are derived. In addition, we also consider MD multirate filter banks without checkerboard effect. Simulation examples show that the checkerboard effect can be avoided by using the proposed conditions.

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.