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Reduced execution time and increased power efficiency are important objectives in the distributed execution of collaborative signal processing tasks over wireless sensor networks. The power-efficient implementation of the Fourier transform computation is an exemplar of distributed data communication and processing task widely used in the signal processing field. Past work has presented some energy-efficient in-network Fourier transform computation algorithms devised only for uniformly sampled one-dimensional (1D) sensor data. However the circumstance that sensors are randomly distributed over a 2D plane may be more practical, therefore the conventional two-dimensional Fast Fourier Transform (2D FFT) defined for data sampled on uniform grids is not directly applicable in such environments. We address this problem by designing a distributed hybrid structure consisting of local Nonequispaced Discrete Fourier Transform (NDFT) and global FFT computation. Firstly, NDFT method is applied in a suitable choice of clusters to get the initial uniform Fourier coefficients with allowable estimation error bounds. We experiment with classical linear as well as generalized interpolation methods to compute NDFT coefficients within each cluster. A separable 2D FFT is then performed over all these clusters by employing our proposed energy-efficient 1D FFT computation that reduces communication costs using a novel bit index mapping strategy for data exchanges between sensors. The proposed techniques are implemented in a SID net-SWANS platform to investigate the communication costs, execution time, and energy consumption. Our results show reduced execution time and improved energy consumption when compared with existing work.