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Cyclotomic Fast Fourier Transform with Reduced Additive Complexity

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Intelligent Systems Design and Applications (ISDA 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1351))

Abstract

The Fourier transform is a standard system analysis tool for viewing the frequency content of a signal. The Fourier transform of a sequence, commonly referred to as the discrete time Fourier transform. Discrete Fourier Transforms are implemented through efficient fast Fourier Transform (FFT) algorithms. For Finite field special algorithms are constructed. Based on findings very useful method for the working of Fourier Transform over finite field was developed called Cyclotomic fast Fourier Transform (CFFT). The algorithm has less multiplicative complexity, but additive complexity is very high. The main aim of the research paper is to design Cyclotomic fast Fourier Transform with reduced additive complexity. Proposed algorithm reduces common summands in the Multiple Constant Multiplications. The approach used in algorithm is search for occurances identical expressions and replace it with new single variable.The algorithm is advantageous as it resulted in additive complexity reduction, computation of area of constant matrix multiplication with minimum complexity. The presented method is critically compared with existing method and the experimental result shows that the algorithm satisfies less additive complexity with less number of Xor gates.

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Authors and Affiliations

  1. Nagpur University, Hingna Road, Nagpur, India

    Tejaswini Panse, Monica Kalbande & Yashika Gaidhani

  2. Government College of Engineering, Nagpur, India

    Prashant Deshmukh, Monica Kalbande & Yashika Gaidhani

Authors
  1. Tejaswini Panse
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  2. Prashant Deshmukh
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  3. Monica Kalbande
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  4. Yashika Gaidhani
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Editor information

Editors and Affiliations

  1. Scientific Network for Innovation and Research Excellence, Machine Intelligence Research Labs (MIR Labs), Auburn, WA, USA

    Ajith Abraham

  2. Department of Computer Science, Università degli Studi di Milano, Milan, Milano, Italy

    Vincenzo Piuri

  3. Machine Intelligence Research Labs (MIR Labs), Auburn, WA, USA

    Niketa Gandhi

  4. Campus Centre de Créteil, Université Paris-Est Créteil, Créteil, France

    Patrick Siarry

  5. Department of Construction Management and Real Estate, Vilnius Gediminas Technical University, Vilnius, Lithuania

    Arturas Kaklauskas

  6. School of Engineering, Instituto Superior de Engenharia do Porto, Porto, Portugal

    Ana Madureira

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Panse, T., Deshmukh, P., Kalbande, M., Gaidhani, Y. (2021). Cyclotomic Fast Fourier Transform with Reduced Additive Complexity. In: Abraham, A., Piuri, V., Gandhi, N., Siarry, P., Kaklauskas, A., Madureira, A. (eds) Intelligent Systems Design and Applications. ISDA 2020. Advances in Intelligent Systems and Computing, vol 1351. Springer, Cham. https://doi.org/10.1007/978-3-030-71187-0_77

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