The two-dimensional fast Fourier transform (2-D FFT), which has a wide variety of application areas such as digital signal processing, speech recognition, and image processing, requires quite high-speed computing to handle a huge amount of data. Many parallel hardware FFT algorithms have been proposed for various types of parallel computers.
This paper discusses 2-D FFT algorithms which are implemented on an eight-neighbor processor array. These algorithms combine effectively the direct 2-D FFT algorithm and the communication capability of the 8-neighbor processor array. We propose three types of algorithms by taking account of data allocation strategies which are related to the number of processors P and the number of data elements N to be transformed. Algorithm 1 is a parallel FFT for the case N≤P. For N>P, Algorithm 2 and Algorithm 3 are proposed as two data allocation methods: a similarity allocation method and a superposition allocation method, respectively. By evaluating and comparing their processing times, we show that Algorithm 3 is fastest, and that the processor utilization rate is 100%. Further, we show that Algorithm 3 is faster than the algorithm proposed for a four-neighbor (mesh) processor array.
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