Fourier ptychography (FP) is an imaging technique that applies angular diversity functions for high-resolution complex image recovery. The FP recovery routine switches between two working domains: the spectral and spatial domains. In this paper, we investigate the spectral-spatial data redundancy requirement of the FP recovery process. We report a sparsely sampled FP scheme by exploring the sampling interplay between these two domains. We demonstrate the use of the reported scheme for bypassing the high-dynamic-range combination step in the original FP recovery routine. As such, it is able to shorten the acquisition time of the FP platform by ~50%. As a special case of the sparsely sample FP, we also discuss a sub-sampled scheme and demonstrate its application in solving the pixel aliasing problem plagued in the original FP algorithm. We validate the reported schemes with both simulations and experiments. This paper provides insights for the development of the FP approach.