### Abstract

A fast Fourier transform (FFT) algorithm using Fermat number transform (FNT) is proposed, and the economical merit of the FFT processor via the algorithm is presented. The algorithm is based on the following three facts: (1) the DFT of prime transform length turns into discrete cyclic convolution (DCC). (2) The DCC can be computed through the number theoretic transform. (3) When the transform sequence length can be decomposed into the product of mutual prime integers, there exists the direct product of the individual factors of the DFT. Among number theoretic transforms, the FNT can be decomposed easily into modules and can be computed by an efficient algorithm. However, for the method using only (1) and (2) above, the transform length is limited. Using (3) above, the variety of transform length can be introduced. Since the proposed algorithm can be decomposed easily into modules, it may be realized easily in hardware. By computing the number of FNT butterfly and multiplication operations of the algorithm, the hardware cost is evaluated. The method costs approximately half that of the corresponding processor based on the radix-2 FFT.

Original language | English |
---|---|

Pages (from-to) | 12-21 |

Number of pages | 10 |

Journal | SYST COMPUT CONTROLS |

Volume | 13 |

Issue number | 4 |

Publication status | Published - Jul 1982 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*SYST COMPUT CONTROLS*,

*13*(4), 12-21.

**FAST FOURIER TRANSFORM ALGORITHM USING FERMAT NUMBER TRANSFORM.** / Morikawa, Yoshitaka; Hamada, Hiroshi; Yamane, Nobumoto.

Research output: Contribution to journal › Article

*SYST COMPUT CONTROLS*, vol. 13, no. 4, pp. 12-21.

}

TY - JOUR

T1 - FAST FOURIER TRANSFORM ALGORITHM USING FERMAT NUMBER TRANSFORM.

AU - Morikawa, Yoshitaka

AU - Hamada, Hiroshi

AU - Yamane, Nobumoto

PY - 1982/7

Y1 - 1982/7

N2 - A fast Fourier transform (FFT) algorithm using Fermat number transform (FNT) is proposed, and the economical merit of the FFT processor via the algorithm is presented. The algorithm is based on the following three facts: (1) the DFT of prime transform length turns into discrete cyclic convolution (DCC). (2) The DCC can be computed through the number theoretic transform. (3) When the transform sequence length can be decomposed into the product of mutual prime integers, there exists the direct product of the individual factors of the DFT. Among number theoretic transforms, the FNT can be decomposed easily into modules and can be computed by an efficient algorithm. However, for the method using only (1) and (2) above, the transform length is limited. Using (3) above, the variety of transform length can be introduced. Since the proposed algorithm can be decomposed easily into modules, it may be realized easily in hardware. By computing the number of FNT butterfly and multiplication operations of the algorithm, the hardware cost is evaluated. The method costs approximately half that of the corresponding processor based on the radix-2 FFT.

AB - A fast Fourier transform (FFT) algorithm using Fermat number transform (FNT) is proposed, and the economical merit of the FFT processor via the algorithm is presented. The algorithm is based on the following three facts: (1) the DFT of prime transform length turns into discrete cyclic convolution (DCC). (2) The DCC can be computed through the number theoretic transform. (3) When the transform sequence length can be decomposed into the product of mutual prime integers, there exists the direct product of the individual factors of the DFT. Among number theoretic transforms, the FNT can be decomposed easily into modules and can be computed by an efficient algorithm. However, for the method using only (1) and (2) above, the transform length is limited. Using (3) above, the variety of transform length can be introduced. Since the proposed algorithm can be decomposed easily into modules, it may be realized easily in hardware. By computing the number of FNT butterfly and multiplication operations of the algorithm, the hardware cost is evaluated. The method costs approximately half that of the corresponding processor based on the radix-2 FFT.

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UR - http://www.scopus.com/inward/citedby.url?scp=0020150442&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0020150442

VL - 13

SP - 12

EP - 21

JO - Systems, computers, controls

JF - Systems, computers, controls

SN - 0096-8765

IS - 4

ER -