Signal Processing - September 2017 - 188

SDFT
SWIFT
αSWIFT

-10

(dB)

100
80

-20

60
0

-30

-1
-40
-50

-2

5
Time (s)

5.0 5.1 5.2
7

0
8

Instantaneous Chirp Frequency (Hz)

Figure 4. A comparison of an SDFT (N = 100), SWIFT (x = 72.1), and a SWIFT (x slow = 72.1,

x fast = 14.2), with center frequencies at 50 Hz and comparable window lengths, operating on a
chirp signal (fs = 1 kHz).

This corresponds well with the halfmass
of the window. The SWIFT and aSWIFT
behave differently, however, peaking 0.121
s and 0.134 s after the chirp passes 50 Hz,
despite also having halfmasses of 0.05 s.

Summary
The SWIFT algorithm for spectral analysis has been presented and shown to
have several advantages over the SDFT
algorithm, especially for applications
that require successive calculations and
real-time analysis. The SWIFT provides improved stability and frequency
resolution while reducing computational
complexity, memory requirements, and
spectral leakage. Additionally, we pre-

sented the aSWIFT, which further reduces spectral leakage and reduces noise.

Authors
Logan L. Grado (grado@umn.edu) is a
Ph.D. degree candidate in biomedical
engineering at the University of Minnesota. He is broadly interested in the
field of neural engineering, specifically
deep brain stimulation technologies. He
is also working to develop and apply
machine-learning techniques to neurological disorders, such as Parkinson's disease and essential tremor.
Matthew D. Johnson (john5101@
umn.edu) is an associate professor of biomedical engineering at the University of

Minnesota. He received his S.B. degree
in engineering sciences from Harvard
University, Cambridge, Massachusetts, in
2002 and his M.S. and Ph.D. degrees in
biomedical engineering from the University of Michigan in 2003 and 2007,
respectively. Between 2007 and 2009, he
completed a postdoctoral fellowship at
the Cleveland Clinic. His primary research interests are the application of signal processing, control engineering, and
neural interface technology to neuromodulation therapies.
Theoden I. Netoff (tnetoff@umn
.edu) is an associate professor of biomedical engineering at the University of
Minnesota. He received his bachelor's
degree in psychology from the University
of California, Berkeley, and his Ph.D
degree in neuroscience from George
Washington University. His research
focuses on closed-loop therapies to optimize electrical stimulation as applied to
the brain for treatment of Parkinson's disease and epilepsy.

References

[1] T. Springer, "Sliding FFT computes frequency-spectra in real-time," Electr. Design News Mag., vol. 33, no.
20, pp. 161, 1988.
[2] E. Jacobsen and R. Lyons, "The sliding DFT," IEEE
Signal Process. Mag., vol. 20, no. 2, pp. 74-80, 2003.
[3] E. Jacobsen and R. Lyons, "An update to the sliding
DFT," IEEE Signal Process. Mag., vol. 21, no. 1, pp.
110-111, 2004.
[4] R. G. Lyons, Understanding Digital Signal
Procesing. Englewood Cliffs, NJ: Prentice Hall, 2004.
[5] K. Duda, "Accurate, guaranteed stable, sliding discrete fourier transform," IEEE Signal Process. Mag.,
vol. 27, no. 6, pp. 124-127, 2010.
SP

errata

n the July 2017 issue of IEEE Signal
Processing Magazine, an error was
introduced in the title of a feature article

Digital Object Identifier 10.1109/MSP.2017.2727778
Date of publication: 6 September 2017

188

during the production process. The title of
the article by Z. Zhang, N. Cummins,
and B.W. Schuller printed incorrectly
[1]. The correct title is "Advanced Data
Exploitation in Speech Analysis." We
sincerely apologize for this error and any
confusion it may have caused.
IEEE Signal Processing Magazine

September 2017

Reference

[1] Z. Zhang, N. Cummins, and B. W. Schuller,
"Advanced data expoitation in speech analysis," IEEE
Signal Process. Mag., vol. 34, no. 4, pp. 107-129,
July 2017.

Table of Contents for the Digital Edition of Signal Processing - September 2017