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2020•Unpublished venueRequires access

Radix-2/6 and Radix-3/6 FFTs for a Length 6m

Chao Wang, Na Wang, Sian-Jheng

Open publisher page 1 citations

Abstract

We focus on the extensively utilized algorithm for split radix FFT. It proposes two the 6mpoint split radix fast Fourier transform (SRFFT), where the complex numbers are represented in a special basis (1, μ) and μ is the complex cube root of unity. Two SRFFTs, termed radix-2/6 and radix-3/6, are proposed and both algorithms are based on radix 2 and radix 3 FFT. Furthermore, we utilize them to design appropriate algorithm structure for length 6m. In addition, fast multiplication in (1, μ) is also proposed. Compared with prior results, the proposed SRFFT requires fewer real multiplications. To our knowledge, this is the first SRFFTs over the basis (1, μ) and this work achieves better specifications for area use and delay. Meanwhile, the occupied resources are approximately same. Moreover, the performance of different FFT length is analyzed.

About this research paper

What this paper is about

We focus on the extensively utilized algorithm for split radix FFT. It proposes two the 6mpoint split radix fast Fourier transform (SRFFT), where the complex numbers are represented in a special basis (1, μ) and μ is the complex cube root of unity. Two SRFFTs, termed radix-2/6 and radix-3/6, are proposed and both algorithms are based on radix 2 and radix 3 FFT. Furthermore, we utilize them to design appropriate algorithm structure for length 6m. In addition, fast multiplication in (1, μ) is also proposed. Compared with prior results, the proposed SRFFT requires fewer real multiplications. To our knowledge, this is the first SRFFTs over the basis (1, μ) and this work achieves better specifications for area use and delay. Meanwhile, the occupied resources are approximately same. Moreover, the performance of different FFT length is analyzed.

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Available abstract

We focus on the extensively utilized algorithm for split radix FFT. It proposes two the 6mpoint split radix fast Fourier transform (SRFFT), where the complex numbers are represented in a special basis (1, μ) and μ is the complex cube root of unity. Two SRFFTs, termed radix-2/6 and radix-3/6, are proposed and both algorithms are based on radix 2 and radix 3 FFT. Furthermore, we utilize them to design appropriate algorithm structure for length 6m. In addition, fast multiplication in (1, μ) is also proposed. Compared with prior results, the proposed SRFFT requires fewer real multiplications. To our knowledge, this is the first SRFFTs over the basis (1, μ) and this work achieves better specifications for area use and delay. Meanwhile, the occupied resources are approximately same. Moreover, the performance of different FFT length is analyzed.

Key concepts: Radix (gastropod), Fast Fourier transform, Split-radix FFT algorithm, Computer science, Arithmetic, Prime-factor FFT algorithm, Multiplication (music), Twiddle factor

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