Vector Radix 2 × 2 Sliding Fast Fourier Transform

Keun Yung Byun, Chun Su Park, Jee Young Sun, Sung-Jea Ko

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The two-dimensional (2D) discrete Fourier transform (DFT) in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT) algorithm based on the vector radix (VR) 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

Original languageEnglish
Article number2416286
JournalMathematical Problems in Engineering
Volume2016
DOIs
Publication statusPublished - 2016

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Discrete Fourier transform
Fast Fourier transform
Discrete Fourier transforms
Fast Fourier transforms
Bins
Sliding Window
Unconditional Stability
Scenarios
Spectrum Analysis
Numerical Algorithms
Spectrum analysis
Linear Combination
Consecutive
Computational complexity
Lowest
Theoretical Analysis
Computational Complexity
Unstable

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Vector Radix 2 × 2 Sliding Fast Fourier Transform. / Byun, Keun Yung; Park, Chun Su; Sun, Jee Young; Ko, Sung-Jea.

In: Mathematical Problems in Engineering, Vol. 2016, 2416286, 2016.

Research output: Contribution to journalArticle

Byun, Keun Yung ; Park, Chun Su ; Sun, Jee Young ; Ko, Sung-Jea. / Vector Radix 2 × 2 Sliding Fast Fourier Transform. In: Mathematical Problems in Engineering. 2016 ; Vol. 2016.
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