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.

It is found that the supercontinuum spectrum is generated from cross-phase modulated soliton pulses which are propagated through a dispersion-flattened/decreasing fiber with low birefringence. The cross-phase modulation is achieved by exciting two orthogonally polarized modes in a birefringent fiber and the effect of input azimuth of linearly polarized pulses is discussed theoretically and numerically.