Sliding Discrete Fourier Transform for 2D Signal Processing

  • Anita KuchanEmail author
  • D. J. Tuptewar
  • Sayed Shoaib Anwar
  • Sachin P. Bandewar
Conference paper
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 30)


Discrete Fourier Transform (DFT) is the most frequently used method to determine the frequency contents of the digital signals. As DFT will take more time to implement, this paper gives the algorithm for the fast implementation of the DFT on the Two-Dimensional (2D) sliding windows. To fast implement DFT on the 2D sliding window, a 2D DFT (here 2D SDFT) algorithm is stated. The algorithm of the proposed 2D SDFT tries to compute current window’s DFT bins directly. It makes use of precalculated bins of earlier window. For a 2D input signal, sliding transform is being accelerated with the help of the proposed algorithm. The computational requirement of the said algorithm is found to be lowest among the existing ones. The output of discrete Fourier transform and sliding discrete Fourier transform algorithm at all pixel positions is observed to be mathematically equivalent


Discrete Fourier transform Sliding window 2D algorithm 


  1. 1.
    Farhang-Boroujeny B, Gazor S (1994) Generalized sliding FFT and its application to implementation of block LMS adaptive filters. IEEE Trans Sig Process 42(3):532–538CrossRefGoogle Scholar
  2. 2.
    Park C-S (2015) 2D Discrete Fourier transform on sliding windows. IEEE Trans Image Process 24(3):901–907MathSciNetCrossRefGoogle Scholar
  3. 3.
    Jacobsen E, Lyons R (2003) The sliding DFT. IEEE Sig Process Mag 20(2):74–80Google Scholar
  4. 4.
    Duda K (2010) Accurate, guaranteed stable, sliding discrete Fourier transform [DSP tips and tricks]. IEEE Sig Process Mag 27(6):124–127Google Scholar
  5. 5.
    Farhang-Boroujeny HB, Lim V (1992) A comment on the computational complexity of sliding FFT. IEEE Trans Circ Syst-II Analog Digital Sig Process 39(12):875–876CrossRefGoogle Scholar
  6. 6.
    Rosendo Maias JA, Exposito AG (1998) Efficient moving-window DFT algorithms. IEEE Trans Circ Syst -II: Analog Digital Sig Process 45(2):256–260Google Scholar
  7. 7.
    Deng G, Ling A (1996) A running Walsh-Hadamard transform algorithm and its application to isotropic quadratic filter implementation. In: Proceedings of European signal processing conference (EUSIPCO)Google Scholar
  8. 8.
    Mozafari B, Savoji MH (2007) An efficient recursive algorithm and an explicit formula for calculating update vectors of running Walsh Hadamard transform. In: Proceedings of IEEE 9th international symposium on signal processing and its applications (ISSPA)Google Scholar
  9. 9.
    Ben-Artzi G, Hel-Or H, Hel-Or Y (2007) The gray-code filter kernels. IEEE Trans Pattern Anal Mach Intell 29(3):382393CrossRefGoogle Scholar
  10. 10.
    Ouyang W, Cham W-K (2010) Fast algorithm for Walsh Hadamard transform on sliding windows. IEEE Trans Pattern Anal Mach Intell 32(1):165–171Google Scholar
  11. 11.
    Jacobsen E, Lyons R (2004) An update to the sliding DFT. IEEE Signal Process Mag 21(1):110111CrossRefGoogle Scholar
  12. 12.
    Park C, Ko S (2014) The hopping discrete Fourier transform [sp tips and tricks]. IEEE Sig Process Mag 31(2):135–139CrossRefGoogle Scholar
  13. 13.
    Park C-S (2014) Recursive algorithm for sliding Walsh Hadamard transform. IEEE Trans Sig Process 62(11):28272836MathSciNetGoogle Scholar
  14. 14.
    Banks K (2002) The Goertzel algorithm. Embed Syst Program Mag 15(9):3442Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Anita Kuchan
    • 1
    Email author
  • D. J. Tuptewar
    • 1
  • Sayed Shoaib Anwar
    • 1
  • Sachin P. Bandewar
    • 1
  1. 1.Mahatma Gandhi Missions College of EngineeringNandedIndia

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