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An Algorithm for Computing the Radix-2n Fast Fourier Transform

Junyuan Zhang, Zhenhua LI

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Abstract

In digital signal processing, the Fast Fourier Transform (FFT) is a kind of high efficient method to calculate the discrete Fourier transform (DFT). It cuts the discrete signal sequence which the length is N for different radix sequences to operate using the way of handing back and partition. Currently, the radix-2 FFT algorithm is a popular approach to do the transform work. However, its computation is still big. This paper seeks for a more efficient algorithm to better reduce computational complexity and it starts the study from the radix-2 and the radix-4 fast Fourier transform, then explores more efficient and faster radix-8 FFT algorithm and finally extends to radix any power of 2. Experiments evidence that the radix-8 FFT algorithm outperform the radix-2 in all in circumstances, therefore prove the feasibility and efficiency of the radix-2n.

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What this paper is about

In digital signal processing, the Fast Fourier Transform (FFT) is a kind of high efficient method to calculate the discrete Fourier transform (DFT). It cuts the discrete signal sequence which the length is N for different radix sequences to operate using the way of handing back and partition. Currently, the radix-2 FFT algorithm is a popular approach to do the transform work. However, its computation is still big. This paper seeks for a more efficient algorithm to better reduce computational complexity and it starts the study from the radix-2 and the radix-4 fast Fourier transform, then explores more efficient and faster radix-8 FFT algorithm and finally extends to radix any power of 2. Experiments evidence that the radix-8 FFT algorithm outperform the radix-2 in all in circumstances, therefore prove the feasibility and efficiency of the radix-2n.

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Available abstract

In digital signal processing, the Fast Fourier Transform (FFT) is a kind of high efficient method to calculate the discrete Fourier transform (DFT). It cuts the discrete signal sequence which the length is N for different radix sequences to operate using the way of handing back and partition. Currently, the radix-2 FFT algorithm is a popular approach to do the transform work. However, its computation is still big. This paper seeks for a more efficient algorithm to better reduce computational complexity and it starts the study from the radix-2 and the radix-4 fast Fourier transform, then explores more efficient and faster radix-8 FFT algorithm and finally extends to radix any power of 2. Experiments evidence that the radix-8 FFT algorithm outperform the radix-2 in all in circumstances, therefore prove the feasibility and efficiency of the radix-2n.

Key concepts: Split-radix FFT algorithm, Rader's FFT algorithm, Prime-factor FFT algorithm, Fast Fourier transform, Discrete Fourier transform (general), Radix (gastropod), Algorithm, Cooley–Tukey FFT algorithm

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