Identification of Firearm Calibers via Acoustical Signature of the Ejected Cartridge Case

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1 Identification of Firearm Calibers via Acoustical Signature of the Ejected Cartridge Case Luiz Vinícius G. Laborda Larrain 1, Forensic Analysis in Audio-Visual Unit Technical and Scientific Police of Mato Grosso (POLITEC) Cuiabá, Brazil João Paulo C. Lustosa da Costa 1 1 Department of Electrical Engineering (ENE) University of Brasília (UnB) Brasília, Brazil joaopaulo.dacosta@ene.unb.br Tadeu Junior Gross Forensic Analysis in Audio-Visual Unit Technical and Scientific Police of Mato Grosso (POLITEC) Cuiabá, Brazil tadeugross@politec.mt.gov.br Abstract Audio gunshot recordings can be very helpful for crime scene investigation although there are several technical challenges for the forensic experts to extract useful information. In this paper, we focus on a specific mechanical action of the firearms: the ejection of used cartridges. First we propose an acoustical model to the cartridge cases inspired by acoustical physics concepts. In the sequence we validate our proposed model using controlled measurements from four different calibers. In addition, by taking 339 gunshot recordings from YouTube, we show that our proposed scheme can identify the firearm calibers in 75% of the cases. Keywords audio forensics; identification of firearm's caliber; gunshot recordings; I. INTRODUCTION Audio forensics includes crime investigation committed by using firearms. Due to the substantial increase of audio and video recordings with crimes, the techniques of audio forensics should adapt to the new types of scenarios. Audio recordings of gunshots can be very helpful to provide answers to some crucial problems in a crime scene investigation. Some real problems can be the determination of the loud bang as a real gunshot, the firearm caliber's identification, the quantity of different fired guns, the sequence of shooters, and the direction of arrival of a gunshot. Examples of approaches to such problems include the acoustical modeling and characterization of gunshots [-4], gunshot detection in noisy environments [5], the directional aspects of forensic gunshot recordings [6], firearm identification from the gunshot recording [7], shooter localization [8-9] and the firearm identification based on rotation invariant feature of cartridge case []. To perform the analysis of a gunshot recording, the forensic expert must consider the distinct components that constitute the gunshot sound. These components can be classified as the muzzle blast, caused by the explosion of the charge that propels the bullet, the mechanical actions, that are the sounds inherent to the functioning of the gun, like the trigger and hammer mechanism, or the expulsion of used cartridges in some cases, a shock wave from supersonic projectiles, and finally the sounds related to surface vibration that can generally be caused by impulsive sounds, as the sound wave hits the ground or other solid surfaces []. Most approaches frequently focus on the muzzle blast or the shock wave. This work proposes an approach to identify the firearm's caliber via the acoustical signature of the sound caused by the collision of the ejected cartridge case with the floor. To the best of our knowledge, no similar approach has been proposed in the literature. In this paper, inspired by acoustical physics concepts, first we propose an acoustical model to the sound generated when the ejected cartridge cases touch any rigid surfaces like the floor. In the sequence, we validate our proposed model using controlled measurements from four different calibers. In addition, by taking 339 gunshot recordings from YouTube, we show that our proposed scheme can identify the firearm calibers in 75% of the cases. Note that we have published a preliminary result of this study in [1] and now we validate our results for real recordings from YouTube. The paper is organized as follows: Section II shows the physical model adopted to the cartridge case ejection problem while Section III presents experiments with real sound measurements obtained from the collision of the cartridge case on the floor. In Section IV, we validate the theoretical model in Section II with real measurements performed in a controlled laboratory and with real videos obtained from the web. Conclusions are drawn in Section V. II. PHYSICAL MODELING OF THE PROBLEM This section is divided into three subsections. In Subsection II.A, we present an introduction to the eject mechanisms of the ejected cartridges cases. In Subsection II.B, we specify the physical characteristics of the cartridge cases and the dimensions of the calibers delimited in this study. Finally, in Subsection II.C, a model to the acoustical behavior of the delimited calibers is proposed. A. Eject mechanisms of the spent cartridges cases Some categories of firearms such as the semiautomatic and automatic guns have mechanisms to eject the fired cartridge case and load a new cartridge from the magazine into the barrel ready for firing after shooting. As illustrated in Figure 1, this is the case of most of self-loading pistols, submachine guns, self-loading rifles and heavy machine guns /15/$31./ 15 IEEE

2 These ejection mechanisms aim an automatic reloading of ammunition, preparing the firearm for a next shot in a short time. Fig. 1. The ejection of fired cartridge case in a self-loading pistol The method proposed in this paper is preferably applied to automatic firearms since the ejection of the cartridge case does not depend on a volunteer action of the shooter. However, our proposed approach can also be applied to other firearms like revolvers or pump-action rifles, for example, but in these cases a specific action such as reload the revolver or pulling back the fore-end is required. B. Physical characteristics of the cartridge case The cartridge is basically composed by four elements: bullet, propellant, cartridge case and primer as shown in Figure. Cartridge Case Fig.. Components of a centre fire cartridge The main purpose of the cartridge case, other than for holding the components together, is to expand and seal the chamber during firing. This prevents the explosive escape of high-pressure gases through the breech. Cartridge cases are usually made of brass, a composition of 7% copper and 3% zinc. Seldom, they are made of steel, aluminum, plastic or paper. As shown in Figure 3, cartridge cases generally come in three shapes. There are the straight case, where the case diameter is approximately the same along its length, the tapered case, where a wide-based cartridge case is gradually reduced in diameter along its length, and the bottle-necked, where a wide-bodied case is, just beforee the case mouth, reduced in diameter [11]. Fig. 3. Primer Bullet Propellant Shapes: straight case (a), tapered case (b) and bottle-necked (c) In this work, we consider four calibers of pistols: 9 mm Luger, also known as 9 mm Parabellum,.4 S&W,.3 Auto, also known as.3 ACP or 7.65 mm Browning and.38 Auto, also known as.38 ACP or 9 mm short. The dimensions of length, mouth and body diameters of the cartridge cases are indicated in Table I. Caliber TABLE I. Shape 9 mm Tapered Luger case.4 Straight S&W case.3 Auto Straight case.38 Straight Auto case CALIBER'S AND CASE'S DIMENSIONS [1] Total Length (mm) 19 1,56 17,16 17,7 C. Resonant frequencies for open-closed pipes According to acoustical physics concepts, a closed cylindrical air column produces resonant standing waves at a fundamental frequency and at odd harmonics. The closed end is constrained to be a node of the wave and the open end is an antinode as shown in Figure 4. When resonance exists, the displacement is a minimum (node) at the closed end, but the antinode is not exactly at the open end. In practice, the antinode is located a small distance beyond the open end. This extra distance beyond the end of the tube is called the end correction. The acoustic length of the tube is equal to its physical length plus the end correction [13]. The end correction x at the open-end of a cylindrical pipe of diameter D in this work was considered.4 as estimated by [13]. Fig. 4. Standing waves in open-closed pipes To estimate the resonant frequencies, the cartridge cases are considered ideal cylindrical tubes, i. e., perfectly cylindrical and homogeneous. The resonant frequencies are calculated by:, for n = 1, 3, 5... (1). where v, L and D are the speed of sound, length and diameter of the tube, respectively. The theoretical values of the resonant frequencies for each tested caliber are shown in Table II. TABLE II. n =1 n = 3 n = 5 n = 7 Mouth Diameter (mm) Body Diameter (mm) 9,55 9,84,69,74 8,4 8,5 9,45 9, THEORETICAL VALUES OF RESONANT FREQUENCIES CALIBER F 1 (Hz) F 3 (Hz) F 5 (Hz) 9 mm Luger S&W Auto Auto

3 III. EXPERIMENTAL VALIDATION VIA CONTROLLED EXPERIMENTS This section is divided into two subsections. In Subsection III.A, we show the controlled experiments to record real sounds from collision of the fired cartridge case with the floor and, in Subsection III.B, we present the results obtained with focus on the acoustical signature for each A. Experiment Details Analyzing the physical characteristics of the cartridge cases discussed in Section II, there is an apparent similarity with the open-closed tubes model, which suggests they can generate sounds at specific resonant frequencies. To check this hypothesis, controlled experiments were conducted in a closed room with minimized ambient noise. The fired cartridge cases were droppedd individually to approximately 1.6 m from the floor within a circle of radius 1 m with the microphone at the center as depicted in Figure 5. The t 1 and t are the time range, starting at t 1 and finishing at t and N is the number of samples. Then, LTAS as function of frequency can be calculated as: Ψ LTAS, (3) where Ψ i (f) is a power spectral density for i-th windowed frame of signal and L is the total number of frames in which the signal has been divided. Since Ψ (f) is measured in units of Pa /s the LTAS feature has the same units. Finally, we present the results of LTAS as a logarithmic power spectral density (PSD), expressed in db / Hz, relative to P. LTAS B log LTAS /, (4) where P o Pa is considered to be a threshold of human hearing at frequency 1 khz [14]. The LTA spectra obtained for each caliber are shown in curves of Figures 7 to with emphasis for the higher power resonant frequencies. It was verified the predominance of frequencies corresponding to the third component of the theoretical model (F 3 ). Contact of the cartridge case on the floor. Fig. 5. Configuration to acquire the audio of the dropped cartridge cases We used five fired cartridge cases for each one of the studied calibers, except for the 9 mm Luger that was used only three different cartridge cases. Each one of these cases collided at least 5 times with the floor. The audio was recorded in format WAV/PCM, without compression, at 48kHz sample rate with 16 bits resolution and with one channel (mono). B. Spectral Analysis of the Controlled Measurements The spectrograms of the recordings revealed specific and continuous frequencies for all calibers along the controlled measurements. For instance, controlled measurements of the first case of type.38 Auto are shown in Figure 6. It was observed also a significant predominance of one component with greater power over the others. Next the long-term average spectrum (LTAS) is calculated for all controlled measurements and the results are normalized and sorted by each Initially, the power spectral density Ψ i (f) for discrete signal can be calculated using the Discrete Fourier transform (DFT) as follows: Ψ, () where x(n) is the digital audio signal recorded by a microphone and X(k) is the Discrete Fourier transform of x(n). Fig. 6. The higher power resonant frequencies for the first cartridge case of type. 38 Auto In Figure 7 we present the LTAS for the recordings of the 9 mm Luger cartridge cases. There is the occurrence of peaks in the frequency range from 1115 Hz to 115 Hz Fig. 7. LTAS for 9 mm Luger

4 In Figure 8 we present the LTAS for the recordings.4 S&W cartridge cases. There is the occurrence of peaks in the frequency range from 85 Hz to 845 Hz Fig. 8. LTAS for.4 S&W In Figure 9 we present the LTAS for the recordings.3 Auto cartridge cases. There is the occurrence of peaks in the frequency range from 15 Hz to 15 Hz. 6 1 IV. MODEL VALIDATION USING CONTROLLED AND UNCONTROLLED MEASUREMENTS The results obtained through the experiments showed that the acoustical physics concepts hold and there are different acoustical signatures for distinct cartridge cases of the same caliber and material. In addition, significant differences are revealed between distinct calibers. For instance, in Figure 11, there is a superposition of the normalized averages of the LTAS for all calibers delimitedd in this study. The only exception for the calibers tested it is for.3 Auto and.38 Auto, where occurred an overlap between the averages of the LTA spectra. Such similarity was expected since the length of these cases are almost the same as shown in Table I. For the validation of the proposed model, the normalized root-mean-square error (NRMSE) is calculated as follows: NRMSE ², where F 3 and F are the observed and theoretical frequencies respectively and F is the average of the observed frequencies., (5) Fig. 9. LTAS for.3 Auto Fig. 11. Superposition of the normalized averages of the LTAS for all calibers studied In Figure we present the LTAS for the recordings.38 Auto cartridge cases. There is the occurrence of peaks in the frequency range from 1165 Hz to 1195 Hz. The obtained practical results present reasonable adherence to the proposed theoretical model as shown in Table III. The exception occurred for the CBC caliber.4 S&W, which had the highest NRMSE regarding physical modeling proposal. TABLE III. VALIDATION OF THE PROPOSED MODEL Fig.. LTAS for.38 Auto CALIBER Observed Frequencies (Hz) 9 mm Luger 1115 to S&W 85 to Auto 15 to Auto 1165 to 1195 Theoretical Frequencie - F 3 (Hz) NRMSE 1117, , , ,96 In a second part of experiments, we considered data obtained from non-controlled environments such as videos from YouTube containing recordings of gunshots committed by identified pistol calibers 1. 1 Dataset available at:

5 In this selection we considered 339 gunshots recordings, all committed by self-loading pistols, made under variable conditions and different qualities. In all videos collected the pistol calibers were identified by the video s title, verbally by the shooter or even by the subtitles. We assume that the information about the type of gun provided on the video is correct. From the audio of these videos, it was possible to identify the acoustical signature in approximately 75% of the cases as shown in Table IV. We conclude with this analysis that a successful identification of the acoustical signature depends more on the environmental conditions and the quality of the record than the calibers. TABLE IV. IDENTIFICATION OF ACOUSTICAL SIGNATURES CALIBER Total of Acoustical Gunshots Signature Identified Accuracy 9 mm Luger ,75%.4 S&W ,41%.3 Auto ,9%.38 Auto ,38% Total ,63% In Figure 1, we present the histogram of the measured frequencies for firearms identified on videos with 9 mm Luger Histogram of Acoustical Signature - 9 mm Luger Fig. 1. Distribution of frequency in gunshot recordings of 9 mm Luger In Figure 13, we present the histogram of the measured frequencies for firearms identified on videos with.4 S&W Histogram of Acoustical Signature -.4 S&W Fig x Distribution of frequency in gunshot recordings of.4 S&W In Figure 14, we present the histogram of the measured frequencies for firearms identified on videos with.3 Auto Histogram of Acoustical Signature -.3 Auto Fig. 14. Distribution of frequency in gunshot recordings of.3 Auto In Figure 15, we present the histogram of the measured frequencies for firearms identified on videos with.38 Auto Histogram of Acoustical Signature -.38 Auto Fig x 4 Distribution of frequency in gunshot recordings of.38 Auto Note the frequency ranges observed in real cases show high consistency with our experimental results as shown in Figure 11. Among the advantages of the proposed approach are the dispensability of some variables cited in the literature for the interpretation and satisfactory analysis from gunshot in audio forensics, such as the acoustical surroundings of the location; information about the ammunition; the information about wind and humidity; the spatial relationship between the firearm and the microphone [3,6]. These parameters in many cases are unknown by the forensic expert. As shown in Subsection III.B, the analyzed frequencies depend exclusively on material and physical dimensions of the cartridge cases. Therefore, with our proposed technique, additional and crucial information can be exploited by the forensic expert in order to establish important inferences about the crime scene. According to the results obtained in non-controlled measurements, the proposed approach achieves a good detection of the acoustic signatures even in amateur recordings. Hence, our proposed approach is considered very promising in forensic acoustics. x 4

6 V. CONCLUSIONS This work confirmed the hypothesis of the presence of resonant frequencies when the ejected cartridge cases touch a rigid surface just after the gunshot. It was also verified at least one frequency, for each studied calibers, has more significant values of power. The proposed approach is validated for controlled and uncontrolled scenarios. In case of uncontrolled scenarios, a correct detection of 75% has been achieved. Acknowledgment The authors thank the Brazilian research and innovation agencies FAPDF (Research Support Foundation of the Federal District), FINEP (Agreement RENASIC / PROTO ), CAPES and CNPq under the FORTE Project - CAPES Forensic Sciences Announcement 5/14 and under the PVE Project number /13-1 for their financial support on this research. We also thank the directors of Scientific Police of Mato Grosso for supporting the qualification of the forensic experts of this agency via the Forensic Master s Program between the Brazilian Federal Police Department and the University of Brasília. References [1] Larrain, L. V. G. L., da Costa, J. P. C. L. and Gross, T. J. "Identificação do calibre de pistolas por meio da assinatura acústica dos estojos ejetados," In: Proc. International Conference on Forensic Computer Science (ICoFCS'15), Brasília, Brazil, best paper award, 15. [] Maher, R.C. "Modeling and signal processing of acoustic gunshot recordings", In: Proc. IEEE Signal Processing Society 1th Digital Signal Processing Workshop, Jackson Lake, WY, pp , 6. [3] Maher, R.C. "Acoustical characterization of gunshots", In: Proc. IEEE SAFE 7: Workshop on Signal Processing Applications for Public Security and Forensics, Washington, DC, pp , 7. [4] Maher, R.C. and Shaw, S.R. "Deciphering gunshot recordings", In: Proc. AES 33rd Conference Audio Forensics - Theory and Practice, Denver, CO, 8. [5] Freire, I. L. and Apolinario Jr., J. A. "Gunshot detection in noisy environments", In: Proc. 7th International Telecommunications Symposium, Manaus, Brasil,. [6] Maher, R. C. and Shaw, S. R. "Directional aspects of forensic gunshot recording", In: Proc. AES 39th International Conference Audio Forensics - Practices and Challenges, Hillerod, Dinamarca,. [7] Thumwarin, P., Matsuura, T. and Yakoompai, K. "Audio forensics from gunshot for firearm identification", In: Proc. IEEE 4th Joint International Conference on Information and Communication Technology, Electronic and Electrical Engineering, Tailândia, pp. 1-4, 14. [8] Freire, I. L. and Apolinario Jr., J. A. "GCC-based DoA estimation of overlapping muzzleblast and shockwave components of gunshot signals", In: Proc. IEEE Second Latin American Symposium on Circuits and Systems (LASCAS), Bogota, pp. 1-4, 11. [9] Calderon, P., Manolo, D. and Apolinario Jr., J. A. "Shooter Localization based on DoA Estimation of Gunshot Signals and Digital Map Information", In: IEEE (Magazine IEEE Latin America) Latin America Transactions, 13.: , 15. [] Thumwarin, P., Prasit, C., and Matsuura, T. "Firearm identification based on rotation invariant feature of cartridge case", In: Proc. IEEE SICE Annual Conference, Tóquio, Japão, pp , 8. [11] Heard, B. J. "Handbook of Firearms and Ballistics: examining and interpreting forensic evidence", ed., Wiley-Blackwell, 8. [1] Site: " [Acessed: April 15]. [13] Askill, J. "Physics of musical sounds". nd ed., Chapter 7. Available: < chapter7.htm>, 7. [Accessed: May 15]. [14] Lindsay, P. and Norman, P. "Human Information Processing: an Introduction to Psychology", nd ed., Academic Press Inc, 1977.