Vector Radix 2 × 2 Sliding Fast Fourier Transform
Joint Authors
Byun, Keun-Yung
Park, Chun-Su
Sun, Jee-Young
Ko, Sung-Jea
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-01-05
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Byun, Keun-Yung& Park, Chun-Su& Sun, Jee-Young& Ko, Sung-Jea. 2016. Vector Radix 2 × 2 Sliding Fast Fourier Transform. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1111873
Modern Language Association (MLA)
Byun, Keun-Yung…[et al.]. Vector Radix 2 × 2 Sliding Fast Fourier Transform. Mathematical Problems in Engineering No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1111873
American Medical Association (AMA)
Byun, Keun-Yung& Park, Chun-Su& Sun, Jee-Young& Ko, Sung-Jea. Vector Radix 2 × 2 Sliding Fast Fourier Transform. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1111873
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1111873