Two different signal processing algorithms are described for detection and classification of acoustic signals generated by firearm discharges in small enclosed spaces. The first is based on the logarithm of the signal energy. The second is a joint entropy. The current study indicates that a system using both signal energy and joint entropy would be able to both detect weapon discharges and classify weapon type, in small spaces, with high statistical certainty.
References
1.
M.
Hughes
, “Analysis of ultrasonic waveforms using Shannon entropy
,” Proc. - IEEE Ultrason. Symp.
2
, 1205
–1209
(1992
).2.
M.
Hughes
, “Analysis of digitized waveforms using Shannon entropy
,” J. Acoust. Soc. Am.
93
(4
), 892
–906
(1993
).3.
M.
Hughes
, “NDE imaging of flaws using rapid computation of Shannon entropy
,” Proc. - IEEE Ultrason. Symp.
2
, 697
–700
(1993
).4.
M.
Hughes
, “Analysis of digitized waveforms using Shannon entropy. II. High-speed algorithms based on Green's functions
,” J. Acoust. Soc. Am.
95
(5
), 2582
–2588
(1994
).5.
M. S.
Hughes
, J. N.
Marsh
, C. S.
Hall
, D.
Savoy
, M. J.
Scott
, J. S.
Allen
, E. K.
Lacy
, C.
Carradine
, G. M.
Lanza
, and S. A.
Wickline
, “Characterization of digital waveforms using thermodynamic analogs: Applications to detection of materials defects
,” IEEE Trans. Ultrason., Ferroelectr., Frequency Control
52
(9
), 1555
–1564
(2005
).6.
M.
Hughes
, J.
McCarthy
, J.
Marsh
, and S.
Wickline
, “Joint entropy of continuously differentiable ultrasonic waveforms
,” J. Acoust. Soc. Am.
133
(1
), 283
–300
(2013
).7.
M.
Hughes
, J.
McCarthy
, P.
Bruillard
, J.
Marsh
, and S.
Wickline
, “Entropic vs. energy waveform processing: A comparison based on the heat equation
,” Entropy
17
(6
), 3518
–3551
(2015
).8.
J. N.
Marsh
, J. E.
McCarthy
, M.
Wickerhauser
, J. M.
Arbeit
, R. W.
Fuhrhop
, K. D.
Wallace
, G. M.
Lanza
, S. A.
Wickline
, and M. S.
Hughes
, “Application of real-time calculation of a limiting form of the renyi entropy for molecular imaging of tumors
,” IEEE Trans. Ultrason., Ferroelectr. Frequency Control
57
(8
), 1890
–1895
(2010
).9.
J. N.
Marsh
, K. D.
Wallace
, G. M.
Lanza
, S. A.
Wickline
, M. S.
Hughes
, J. E.
McCarthy
, and M. V.
Wickerhauser
, “Application of a limiting form of the Renyi entropy for molecular imaging of tumors using a clinically relevant protocol
,” Proc. - IEEE Ultrason. Symp.
1
, 53
–56
(2010
).10.
K. D.
Wallace
, J.
Marsh
, S. L.
Baldwin
, A. M.
Connolly
, K.
Richard
, G. M.
Lanza
, S. A.
Wickline
, and M. S.
Hughes
, “Sensitive ultrasonic delineation of steroid treatment in living dystrophic mice with energy-based and entropy-based radio frequency signal processing
,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control
54
(11
), 2291
–2299
(2007
).11.
M.
Hughes
, J.
Marsh
, K.
Wallace
, T.
Donahue
, A.
Connolly
, G. M.
Lanza
, and S. A.
Wickline
, “Sensitive ultrasonic detection of dystrophic skeletal muscle in patients with Duchenne's muscular dystrophy using an entropy-based signal receiver
,” Ultrasound Med. Biol.
33
(8
), 1236
–1243
(2007
).12.
M.
Hughes
, J.
Marsh
, K.
Agyem
, J.
McCarthy
, B.
Maurizi
, M.
Wickerhauser
, K.
Wallace
, G.
Lanza
, and S.
Wickline
, “Use of smoothing splines for analysis of backscattered ultrasonic waveforms: Application to monitoring of steroid treatment of dystrophic mice
,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control
58
(11
), 2361
–2369
(2011
).13.
R.
Seip
, E.
Ebbini
, and M.
O'Donnell
, “Non-invasive detection of thermal effects due to highly focused ultrasonic fields
,” Proc. - IEEE Ultrason. Symp.
2
, 1229
–1232
(1993
).14.
R.
Maher
, “Acoustical characterization of gunshots
,” in Signal Processing Applications for Public Security and Forensics, 2007. SAFE'07. IEEE Workshop on, Signal Processing Applications for Public Security and Forensics
(IEEE
, Hoboken, NJ
, 2007
), pp. 1
–5
.15.
P.
Sinha
, S.
Kumar
, and R.
Hegde
, “Sniper localization using passive acoustic measurements over an ad-hoc sensor array
,” in 2015 Twenty First National Conference on Communications (NCC)
(IEEE
, Hoboken, NJ
, 2015
), pp. 1
–6
.16.
M.
Khalid
, M.
Babar
, M.
Zafar
, and M.
Zuhairi
, “Gunshot detection and localization using sensor networks
,” in 2013 IEEE International Conference on Smart Instrumentation, Measurement and Applications (ICSIMA)
(IEEE
, Hoboken, NJ
, 2013
).17.
R.
Maher
, “Audio forensic examination
,” IEEE Signal Process. Mag.
26
(2
), 84
–94
(2009
).18.
A.
Ramos
, S.
Holm
, S.
Gudvangen
, and R.
Otterlei
, “A modified spectral subtraction algorithm for real-time noise reduction applied to gunshot acoustics
,” in 2012 International Conference on Signals and Electronic Systems (ICSES)
(IEEE
, Hoboken, NJ
, 2012
), pp. 1
–5
.19.
T.
Ahmed
, M.
Uppal
, and A.
Muhammad
, “Improving efficiency and reliability of gunshot detection systems
,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(IEEE
, Hoboken, NJ
, 2013
), pp. 513
–517
.20.
A.
Chacn-Rodrguez
, P.
Julin
, L.
Castro
, P.
Alvarad
, and N.
Hernndez
, “Evaluation of gunshot detection algorithms
,” IEEE Trans. Circuits Syst.
58
(2
), 363
–373
(2011
).21.
H.
Zhao
and H.
Malik
, “Audio recording location identification using acoustic environment signature
,” IEEE Trans. Inf. Forensics Secur.
8
(11
), 1746
–1759
(2013
).22.
P.
Bevington
, Data Reduction and Error Analysis for the Physical Sciences
, 1st ed. (McGraw-Hill
, New York
, 1969
), pp. 1
–336
.23.
D. L.
Sackett
, “Why randomized controlled trials fail but needn't: 2. Failure to employ physiological statistics, or the only formula a clinician-trialist is ever likely to need (or understand!)
,” Can. Med. Assoc. J.
165
(9
), 1226
–1237
(2001
).24.
M.
Hughes
, J.
McCarthy
, P.
Bruillard
, J.
Marsh
, and S.
Wickline
, “Entropic vs. energy waveform processing: A comparison based on the heat equation
,” in Proceedings of the Fall 2014 Acoustical Society Meeting
(ASA
, Melville, NY
, 2014
).25.
National Center for Education Statistics, Digest of Education Statistics (U. S. Department of Education, Alexandria, VA,
2015
), Chap. 2.2016
U.S. Government
You do not currently have access to this content.