Signal Processing - September 2017 - 183

mathematics and natural sciences faculty of South-West University, Blagoevgrad, Bulgaria. He is the author of
two books and more than 60 articles,
conference papers, and research works
in mathematical logics, Hausdorff's
approximations, and bioinformatics.
Alexey K. Stefanov (astef@abv.bg)
has been an associate professor with the
technical faculty of South-West University, Blagoevgrad, Bulgaria, since 2012.
He was a previously deputy director of
the Telecommunication Department, the
Telecommunication Department of the
Ministry of Interior, Sofia, Bulgaria. His
research interests include digital audio
and video processing and devices. He is
the author of two books and more than 40
articles, as well as the chief designer of
10 constructive developments.

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FIGURE 5. A circular 2-D filter.

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References

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[1] W. S. Lu and A. Antoniou, Two-Dimensional
Digital Filters. New York: Marcel Dekker, 1992.

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[2] J. S. Lim and A. Antoniou, Two-Dimensional
Signal and Image Processing. Englewood Cliffs, NJ:
Prentice Hall, 1990.

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[3] S. Kockanat and N. Karaboga, The Design
Approaches of Two-Dimensional Digital Filters
Based on Metaheuristic Optimization Algorithms: A
Review of the Literature. New York: Springer-Verlag,
2015, pp. 265-287.

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[4] X. Y. Hong, X. P. Lai, and R. J. Zhao, "Matrixbased algorithms for constrained least-squares and minimax designs of 2-d FIR filters," IEEE Trans. Signal
Process., vol. 64, no. 14, pp. 3620-3631, July 2013.

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[5] L. Andrews, Special Functions of Mathematics for
Engineers. London, U.K.: Oxford Univ. Press, 1998.

FIGURE 6. A fan 2-D filter.

Logan L. Grado, Matthew D. Johnson, and Theoden I. Netoff

The Sliding Windowed Infinite Fourier Transform

T

he discrete Fourier transform (DFT)
is the standard tool for spectral
analysis in digital signal processing, typically computed using the fast
Fourier transform (FFT). However, for
real-time applications that require recalculating the DFT at each sample or over
Digital Object Identifier 10.1109/MSP.2017.2718039
Date of publication: 6 September 2017

only a subset of the N center frequencies
of the DFT, the FFT is far from optimal.
The sliding DFT (SDFT), first developed by Springer in 1988 [1] and then
improved and popularized by Jacobsen
and Lyons in 2003 [2], [3], is an algorithm
that computes individual DFT bins recursively, allowing for efficient computation
of the DFT on a sample-by-sample basis.
The SDFT is efficient; however, it is lim-

1053-5888/17©2017IEEE

IEEE SIGNAL PROCESSING MAGAZINE

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September 2017

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ited in that it is only marginally stable
and requires storing N previous inputs.
Furthermore, the SDFT's rectangular
window causes spectral leakage and is
limited to computing the N center frequencies of the DFT.
Here, we present a novel sliding discrete-time Fourier transform (DTFT),
which we call the sliding windowed infinite Fourier transform (SWIFT), that
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Table of Contents for the Digital Edition of Signal Processing - September 2017
