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This paper presents parallel FFT algorithms with different degree of computation and communication overheads for multiprocessors in a Network-on-Chip (NoC) environment. Of the three parallel FFT algorithms presented in this paper, we propose two parallel FFT algorithms for a 2D NoC that can contain a variable number of processing elements (PEs) and one is a reference parallel FFT algorithm for comparison. A parallel FFT algorithm we propose increases performance by assigning well-balanced computation tasks to PEs. The execution times are reduced because the algorithm uses data locality well to avoid unnecessary data exchanges among PEs and removes the overall idle periods by2 a balanced task scheduling. An enhanced version of this algorithm is suggested in which communication traffic is reduced. In this algorithm, returning transformed data to an original PE after one computation stage before sending them to a next PE for the following stage is removed. Instead, we propose a method that enables to keep regularity of the data communication and computations with twiddle factors. According to the simulation result from our cycle-accurate SystemC NoC model with a parametrizable 2-D mesh architecture, and the analysis of the algorithms in time and complexity, our proposed algorithms are shown to outperform the reference parallel FFT algorithm and FFT implementations on TI Digital Signal Processors (DSPs) that have similar specifications to our simulation environment. [ABSTRACT FROM AUTHOR]