Multiplierless unified architecture for mixed radix-2/3/4 FFTs

Abstract

Abstract-This paper presents a novel runtime-reconfigurable, mixed radix core for computation 2−, 3−, 4− point fast Fourier transforms (FFT). The proposed architecture is based on radix-3 Wingorad Fourier transform, however multiplication is performed by constant multiplication instead of general multiplier. The complexity is equal to multiplierless 3-point FFT in terms of adders/subtractors with the exception of a few additional multiplexers. The proposed architecture supports all the FFT sizes which can be factorized into 2, 3, 4 point systems. We also show that the proposed architecture has the same bound on the accuracy as the classical one.

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“…Trivial multiplication can be simply implemented by using shifters and adders, and therefore, its complexity is much lower than that of non-trivial multiplication. Therefore, the mixed-radix algorithm can be implemented with lower complexity than the radix-2 or radix-4 algorithms can [37]. In addition, it can support more flexible FFT lengths than the radix-4 or radix-8 algorithms, and is has double the throughput of the radix-2 3 algorithm.…”