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首页> 外文期刊>IEEE transactions on circuits and systems . I , Regular papers >New radix-(2×2×2)/(4×4×4) and radix-(2×2×2)/(8×8×8) DIF FFT algorithms for 3-D DFT
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New radix-(2×2×2)/(4×4×4) and radix-(2×2×2)/(8×8×8) DIF FFT algorithms for 3-D DFT

机译:用于3-D DFT的新的基数(2×2×2)/(4×4×4)和基数(2×2×2)/(8×8×8)DIF FFT算法

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摘要

In this paper, new three-dimensional (3-D) radix-(2×2×2)/(4×4×4) and radix-(2×2×2)/(8×8×8) decimation-in-frequency (DIF) fast Fourier transform (FFT) algorithms are developed and their implementation schemes discussed. The algorithms are developed by introducing the radix-2/4 and radix-2/8 approaches in the computation of the 3-D DFT using the Kronecker product and appropriate index mappings. The butterflies of the proposed algorithms are characterized by simple closed-form expressions facilitating easy software or hardware implementations of the algorithms. Comparisons between the proposed algorithms and the existing 3-D radix-(2×2×2) FFT algorithm are carried out showing that significant savings in terms of the number of arithmetic operations, data transfers, and twiddle factor evaluations or accesses to the lookup table can be achieved using the radix-(2×2×2)/(4×4×4) DIF FFT algorithm over the radix-(2×2×2) FFT algorithm. It is also established that further savings can be achieved by using the radix-(2×2×2)/(8×8×8) DIF FFT algorithm.
机译:本文提出了新的三维(3-D)基数-(2×2×2)/(4×4×4)和基数-(2×2×2)/(8×8×8)抽取-开发了频率内(DIF)快速傅里叶变换(FFT)算法,并讨论了其实现方案。通过在使用Kronecker乘积和适当的索引映射的3-D DFT计算中引入radix-2 / 4和radix-2 / 8方法来开发算法。所提出的算法的蝶形特征在于简单的封闭形式的表达式,从而简化了算法的软件或硬件实现。比较了所提出的算法和现有的3-D基数(2×2×2)FFT算法,结果表明,在算术运算,数据传输和旋转因子评估或访问查询的次数方面,大量节省可以使用基数(2×2×2)/(4×4×4)DIF FFT算法而不是基数((2×2×2)FFT算法)来实现该表。还可以确定,通过使用基数-(2×2×2)/(8×8×8)DIF FFT算法,可以进一步节省成本。

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