一种小面积的基-3蝶形单元设计
A Small-Area Design of Radix-3 Butterfly Unit
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摘要: 为减少该蝶形单元在硬件实现中的资源消耗,提出了一种基于单精度浮点运算的基-3蝶形单元设计. 采用兼容缩放的方法来解决该蝶形单元中乘法运算,其中√3采用的缩放因子为2<sup<23</sup<. 与√3的乘法操作采用有限个定点加法器来实现. 通过理论分析,该方法减少了加法器的个数,同时减少了寄存器的数量. 通过对比得出,本文采用的方法在原有的基础上减少了1个加法器和2个48位寄存器. 此外,基-3蝶形单元采用降低乘法操作数目的实现形式,使得与实数相乘的乘法数目由原来的4个降为2个. 实验结果表明,本文采用的方法节省了基-3蝶形单元实现所需的硬件资源,为降低基-3FFT实现的资源消耗打下了基础.Abstract: A new technique for radix-3 FFT butterfly unit based on floating-point operation is proposed. The aim of the new design is to reduce the hardware resources. First, compatible scaling is used to solve the multiplication. Let the scale factor of √3 be 2<sup<23</sup<, so the multiplication with √3 is replaced by several fixed-point additions. By theoretical analysis, the proposed method decreases the numbers of adders and registers. By contrast, the proposed design reduces one fixed-point adder and two 48-bit registers. In additional, a structure of radix-3 FFT butterfly unit is adopted and in this structure, the number of multiplications with a real data is reduced from 4 to 2. Experimental results show that the proposed method indeed reduces the hardware resources, which plays an important role in decreasing the resources of radix-3 FFT.
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