Evaluation of Gunshot Detection Algorithms

Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 Evaluation of Gunshot Detection Algorithms Alfonso Chacón-Rodrı́guez Pedro Julián1 Laboratorio de Componentes Electrónicos, Universidad Nacional de Mar del Plata, Argentina Email: alchacon@itcr.ac.cr Instituto de Investigaciones en Ingenierı́a Eléctrica IIIE (UNS-CONICET) Departamento de Ingenierı́a Eléctrica y de Computadoras Universidad Nacional del Sur Avda. Alem 1253, (8000) Bahı́a Blanca Argentina Email: pjulian@uns.edu.ar Signal at 030m, Gun= Pi9a Abstract— Five pre-processing algorithms for the detection of firearm gunshots are statistically evaluated, using the Receiver Operating Characteristic method, as a previous feasibility metric for their implementation on a low power VLSI circuit. 1 0.8 I. I NTRODUCTION Detection, classification and localization of gunshots are of particular interest in areas related to public health, surveillance, law enforcement and the military. There is plenty of research regarding gunshot theory and the needs for its study (see [1]–[4]), as well as many software and hardware implementations of computationally efficient signal processing analysis methods [5]–[10], [22]. These solutions mostly use complex algorithms such as short time Fourier Transforms, Wavelet Transforms, Hidden Markov Models, Gaussian Mixtures and Maximum Likelihood Models and claim to be very effective at detecting, classifying and localizing shots from different firearms. Yet such algorithms are expensive in terms of power due to their computation needs, which range from whole personal computer systems to mote oriented sensor networks with DSP dedicated chips, making their deployment on the field cumbersome when not totally restricted to indoor use. One particular instance of interest is the establishment of a surveillance network against illegal hunting in tropical forest reserves. In such environment, low power sensor networks provide a feasible solution considering the large areas to be protected, and the near impossibility of providing the sensors with standard long lasting power supplies. Though there are some commercial solutions available in that area (see [4], [9], [11]), all of them entail the use of equipment and algorithms that claim to be efficient in terms of processing but not in terms of power dissipation, questioning the use of complex classification methods at least in the early stages of detection. Regarding the complexities behind gunshots and firearms detection and classification, Maher offers a very thorough explanation of the physics of a gunshot in [1]. Gunshot sound is produced by two phenomena. First, the muzzle blast, that is produced by the rapidly expanding gases from the confined explosive charge that is used to propel the bullet out of the gun barrel. This acoustic disturbance lasts 3-5 milliseconds and propagates through the air at the speed of sound. Second, 1 P. Julián is also with CONICET, Av. Rivadavia 1917, Bs. As., Argentina ISBN 978-987-655-003-1 EAMTA 2008 49 Amplitude (normalized) 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 2.48 2.5 2.52 2.54 2.56 2.58 2.6 Time (seconds) 2.62 2.64 2.66 2.68 Fig. 1. Typical time signature of a gunshot: 9mm pistol at 30mts range from the recording microphone. Multipath distortion is appreciated a few miliseconds after the first peak. if the bullet travels at supersonic speed, it causes an acoustic shock wave that propagates away from the bullet’s path. The shock wave expands as a cone behind the bullet, with the wave front propagating outward at the speed of sound. A typical gunshot signature is shown in Fig. 1. The sound characteristics of any gunshot, thus, are determined by factors such as the caliber of the bullet and the barrel, the length of the latter and the chemical properties of the propellant. Besides, being a nearly perfect impulsive signal, any particular measurement of the spectral or impulsive characteristics of a particular gunshot will likely give more information about the acoustic surroundings (i.e., the acoustic impulse response) rather than the firearm or the projectile characteristics [1], which in turn are dependent on another multiple set of factors such as temperature, wind speed, foliage density, air moisture and soil characteristics [12]. Attempts at detecting the Nshaped shock wave (as Sadler et al report using a wavelet approach [7]) become difficult as the wave rapidly loses its shape due to non-linear dispersion, or disappears altogether once the bullet’s speed falls under supersonic speed or hits an obstacle, a possibility which is higher in such a dense setting as a tropical rain forest. On the other hand, looking IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply. Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 A Receiver Operating Characteristic plot is to be obtained for each pre-processing method. According to signal detection theory [14], the ROC plot is constructed with the ordered pairs (TPR, FPR) of a detection system as a function of a certain detection threshold, where TPR stands for True Positive Rate, and FPR for False Positive Rate, and each figure is defined according to at the power spectra of three particular gunshots gives also an idea of the differences between firearms located at the same distance (Fig. 2), which simply discourages the use of a simple filtering method for the task of detection. Therefore, a previous evaluation of the efficiency of any detection algorithm and the feasibility of its low power implementation becomes mandatory before proposing a particular solution. The paper is organized as follows: Section II depicts the typical basic detection architecture; Section III explains the algorithms to be evaluated; Section IV shows the analysis of the results; finally, Section V presents the conclusions. −3 Energy 2 TPR = FPR = 1 0 0 500 1000 1500 2500 2000 4000 3500 3000 Freq. (Hz) Energy Spectrum of a Pi9 at 30mts Energy 0.04 0.02 0 0 500 1000 1500 2500 2000 4000 3500 3000 Freq. (Hz) Energy Spectrum of a S12 at 30mts Energy 0.1 0.05 0 0 500 1000 1500 2500 2000 4000 3500 3000 Freq. (Hz) Fig. 2. Example of the power spectra for a .22 carbine, a 9mm pistol and a .12 shotgun recorded at 30mts. II. BASIC D ETECTION A RCHITECTURE S PECIFICATIONS AND ROC The proposed detection scheme is shown in Fig. 3 and is common in the field of biomedical engineering for the detection of neural spikes [13] but also in other applications involving detection and classification of impulsive audio events [5]. Detection is achieved by the comparison between a preprocessed version of the signal and an adaptive threshold, typically a running average or RMS estimation of the same pre-processed signal, scaled by a gain factor C. x(t) Pre Processing C Detection Running Average Fig. 3. Basic structure of the detection algorithm ISBN 978-987-655-003-1 EAMTA 2008 (1) Total number of negatives A true positive is to be considered as such whenever a detection occurs within a few tens of samples of a real gunshot peak impulse. The evaluation is based on the ordered pair which stands closer (in terms of the Euclidean distance) to a perfect detector with a (TPR,FPR)=(1,0), where FPR gives the xaxis coordinate and TPR gives the y-axis coordinate. Usually, effective detectors are chosen allowing for a certain percentage of FPR in order to increase the TPR, since a false positive can always be eliminated later on by the classification system, while a missing true positive is lost forever. In our case, nonetheless, a detector with a high FPR implies power waste. Besides, it is assumed that the sensor network redundancy can compensate for a certain number of missing true positives. Thus, a sensor with a relatively low TPR may be acceptable for our purposes. Due to the intensive computation involved, a discrete ROC with 5 threshold values is to be calculated for each method and the best pair is to be extracted from the plot. The signals used in the evaluation are a collection of sounds recorded in a dense tropical rain forest, at a 48kHz sampling rate with 32-bit quantization, on a high quality digital recorder, using a professional, high sensitivity, directional microphone. Amplitude is normalized to a maximum pressure of 110dBSP L. The target samples include 5 firearms of different calibers, fired at 30mts, 90mts and 250mts from the recording equipment, at angles of 0◦ , 90◦ and 180◦ . Additional samples for negative validation include: a chain-saw recorded at 30mts from the equipment, at the same three angles as the firearms; two planes low flying over the scene; three recordings of various birds singing; two recordings of rainshowers; recordings of two different water streams; a recording of wind through the trees surrounding the setting; a Matlab generated white noise signal with σ 2 = 0.1; and a male human voice recorded close to the microphone at a normal speech level. All the signals are pre-filtered using an IIR 4th order Butterworth low pass filter with a cutoff frequency of 3KHz (cutoff frequency determined from the observation of the gunshots’ power spectra), except those that are to be processed using wavelets, where the filtering is done by the pre-processing itself. In the case of the negative samples, signals are taken to amplitude levels equivalent to sound pressures ranging between 90dBSP L and 98dBSP L (the typical pressure levels of gunshots at distances greater than 90 mts from the gun barrel, on a obstacle-free propagation environment). Energy Spectrum of a C22 at 30mts x 10 True positives detected Total number of positives False positives detected 50 IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply. Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 III. D ESCRIPTION OF for the analog shift register. The search window, nonetheless, must be limited in length, as this structure quickly degrades the signal [18]. By extensive simulation with the available gunshots’ data, a maximum difference between the peak of the signal and the normalized energy is searched for a low enough value of window length and a specific delay. From the results plot, it is possible to determine that a window size of 7 samples with a delay of 1ms between samples, at a 7kHz sampling rate, is adequate (Fig. 6 shows one of the plots used for the determination of these parameters: it is clear that beyond 1ms, the improvement in the differences of energy is not significant). P RE - PROCESSING A LGORITHMS The following methods are proposed alternatively in [5], [13], and [22]. Detection with no signal pre-processing is taking as floor reference, as Obeid and Wolf do [13]. Implementation complexity is not taken into consideration in the comparison figures, yet an intuitive evaluation of the method hardware feasibility is offered. A. Absolute Value Absolute value of the input signal is taken before being introduced into the detection scheme of Fig. 3. Since abs[x(t)] is a one to one mapping of the energy estimation of the signal (x2 (t)), their respective performances are considered to be equivalent (as Obeid and Wolf argue in [13]), but with a lower implementation complexity. Besides, such pre-processing can be performed by an analog circuit, with the respective power savings involved. x(t) φ1 B. Median Filter Energy e(t) = abs[x(t)] Data direction φ1 φ2 n=3 φ2 n=N φ2 φ1 Fig. 5. Simplified Bucket Brigade Device used as an analog shift register. φ1 and φ2 are complementary phases of a bi-phase sampling clock. Data is fed through a median filter with a window size of 7 samples (3 samples before and 3 samples after the center of the window), with a 1ms delay within each window sample. The filter output is subtracted from the signal in the middle of the window; this is considered as the normalized energy that enters into the threshold unit (Fig. 4). Dufaux et all [5] proposed this structure using a median filter with a window size of 20 samples, using a 44.1kHz sampling rate with 24-bit data resolution. No detail is offered in their paper about the delay within the samples, which we assumed to be equal to the sampling period. x(t) n=2 n=1 Normalized Max Energy and RMS at030m, Window=7 0 10 9mm Pistol 9mm Pistol RMS .32 Revolver .32 Revolver RMS .38 Revolver .38 Revolver RMS .12 Shotgun .12 Shotgun RMS .22 Carbine .22 Carbine RMS −1 energy 10 −2 10 −3 10 Normalized energy Detection Analog Reg. Discrete Median filter −4 10 Running Average 10 10 time (seconds) Fig. 6. Example of search for the optimum delay: median filter with a search window of 7 samples med[e(n)] C. Teager Energy Operator Fig. 4. Median Filter structure. Since there is a one to one relation between x2 (t) y abs[x(t)], the second method is used as it is easier to implement in analog or mixed signal circuits The Teager Energy Operator (TEO), as defined in [19], is applied to the signal before feeding it to the threshold unit. This operator has the following discrete form: For our purposes, a digital implementation is not possible due to its high power requirements. A completely analog implementation as in [16] and [17] is constrained by the delays imposed by the search window, which is in the order of 1ms. Typical analog versions of delay chains are based on allpass filters, that at best provide delays equivalent to a phase shift of up to π radians of the input signal. Besides, delay constants in the order of hundreds of microseconds require RC relations hard to achieve on standard CMOS processes. A mixed-signal approach is therefore a reasonable alternative. A bucket-brigade device (Fig. 5) is a good compromise solution ISBN 978-987-655-003-1 EAMTA 2008 −2 −3 −4 10 y(n) = x(n)2 − (x(n − 1)x(n + 1)) (2) which, as reported by [19], enhances the high frequency components of the input signal x(n), and is thus recommended for the detection of impulsive signals. One advantage of this method is that it can be implemented by an analog circuit, following the continuous equation also proposed in [19]: y(t) = x2 (t) − x(t) 51 d2 x(t) dt IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply. (3) Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 the coefficients decomposition algorithm used in these kind of filter banks (see Bultheel, [23]), a signal f (t) is decomposed in a sum of functions of the type X fj = vjk ϕjk , vj = (vjk ) ∈ ℓ2 (Z) D. Correlation Against a Template Detection and classification methods based on correlation matching are common in plenty of fields, from brain machine interfaces [13] to Ultra Wide Band receivers [20]. Digital simplified detectors based on correlation with very low power dissipation have been successfully built for particular applications [21] and mixed signal general classifiers have also been proposed [18]. Here, a full scale method is initially proposed (floating point resolution, 48kHz sampling rate) as a top metric for the evaluation of the method’s efficiency. On a later stage, simplifications such as the use of integer arithmetic with low resolution or a lower sampling may be introduced, in order to gauge the trade-offs between the degrading efficiency of the method and its hardware feasibility. x(t) k gj = X k wjk ψjk , wj = (wjk ) ∈ ℓ2 (Z) where ϕ(t) is a Riez basis and ψ(t) is an orthonormal basis (both are often referred to as scale father function and wavelet mother function) with both respectively spanning the spaces Vn y Wn , the approximation and detail coefficients of a level n are related to those of the next level n + 1 by the equations: X h̄l−2k vn+1,l vnk = wnk Antialias filter l X = Detection Analog Reg. .... ḡl−2k vn+1,l These equations correspond to the respective P application of P transfer filters with H(z) = k hk z k and G(z) = k gk z k √ functions,√followed by sub-sampling, where hk = ck / 2 and gk = dk / 2, with ck y dk as the coefficients from the dilation equation X X ϕ(t) = ck ϕ(2t − k), ck = 2 (6) Running RMS k .... k and the wavelet equation X ψ(t) = dk ψ(2t − k), dk = (−1)k c̄1−n Template (7) k Basic scheme for a discrete correlation-based detection algorithm. cD1 = wn−1 fn = vn The structure of detection is shown in Fig. 7. First, two signal templates are obtained by the averaging of gunshot signals at 30mts and 90mts, as Obeid and Wolf propose [13]. The templates are stored in two 1000-samples long vectors. Signal is fed through a window the same size of the template vectors, at a rate of 39 samples per iteration. At each iteration, correlation with each vector is computed and stored in another pair of vectors. These are the outputs of the system, which go to a threshold detector. Since the correlation is a signed operation, the averaging is done using a running RMS scheme. In Edwards and Cauwenberghs proposal of a mixed mode classifier implementation of this algorithm [18], the computation is not done directly on the signal itself but on the features provided by a wavelet, cochlear or any other kind of pre-processing algorithm. The sampling vector used is a BBD structure and the correlation is done by analog current multiplication. Just as in the median filter case, the BBD cannot be extremely long. This entails a shortening of the template as well, and a cut on the sampling frequency. G ↓2 H ↓2 cD2 = wn−2 G ↓2 cDN = wn−N cA1 = vn−1 ↓2 H G ↓2 cAN = vn−N cAN − 1 = vn−N −1 H ↓2 Fig. 8. General structure of a wavelet decomposition bank filter. Signal details are given by the wn coefficients . Signal is approximated by the vn coefficients f (t) cD3 ↑2 cD4 ↑2 P Filter Bank E. Discrete Wavelet Transform cD5 Istrate et all proposed in [22] the use of discrete analysis with a Daubechies wavelet of six vanishing moments for the detection of impulsive signals. In our case, we use a similar approach, but using an 8 level Haar wavelet bank filter on a 7kHz sub-sampled signal (Fig. 8). According to ISBN 978-987-655-003-1 EAMTA 2008 (5) l Rxy Fig. 7. (4) Detection ↑2 Average Fig. 9. Filter bank structure. Level detail coefficients energy is calculated before feeding them to the energy sum. 52 IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply. Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 ROC. Method= c30, 0, 90 and 180 degrees The filter bank is structured following a dyadic scale using 3500Hz as the Nyquist frequency, and it is fed with input sequences of 2048 samples. The number of levels of the decomposition and the choice of the coefficients of interest are the result of a preliminary analysis with the wavelet interactive toolbox from Matlab. Energy is calculated and added from the chosen coefficients. Various cases are evaluated: the best results are obtained considering levels 3, 4, 5 and levels 4, 5 and 6. The output is then fed to the threshold detector, as in Fig. 9. The choice of Haar functions is based on their simpler form, which allow for a mixed mode implementation using switched capacitors, for instance. A Haar scale function is basically a moving average operator with a transfer function H(z) = (1 + z −1 )/2, while its wavelet function is a moving difference operator with a transfer function G(z) = (1 − z −1 )/2. IV. E VALUATION R ESULTS AND 1 0.9 True Positive Rate 0.8 Fig. 11. 1500 2000 2500 3000 3500 4000 Samples, level 4 Prep.wav : Signal at 250m, Gun= S12c Gain=70 1000 4500 0.7 2000 2500 3000 Frame samples 3500 4000 0.8 4500 5000 Fig. 10. Example of detection of a 12-caliber shotgun at 250mts from detector, using the DWT pre-processing method at a 7kHz sampling rate. Correlations against templates at 30mts or at 90mts were the best pre-processing methods, yielding no false positives. Two false positives existed though in the positive samples, that is, positives that occurred out of the sample window where the signal’s peak impulse lies. Wavelet analysis using coefficients 3, 4 and 5 was second, with no false positives, and a TPR of 0.89, real close to the correlation’s TPR of 0.91. Third was also wavelet analysis, using the coefficients’ information from levels 4, 5 and 6, with a slight decrease in detection efficiency. A smoother wavelet would probably have given better results, yet with an increase in implementation complexity. Contrary ISBN 978-987-655-003-1 EAMTA 2008 0.8 0.9 1 ROC. Correlation pre-processing with a 30mts template Method TPR FPR Threshold Gain C Correlation 30mts template 0.91 0 25 Correlation 90mts template 0.91 0 25 DWT Coeffs. 3, 4, 5 0.89 0 80 DWT Coeffs. 4, 5, 6 0.87 0.07 70 Median Filter 0.8666 0.1333 25 Absolute value 0.8444 0.1333 15 TEO 0.80 0.20 45 No pre-processing 0.77 0.1333 15 to the correlation method, with wavelet pre-processing there were no false positives in the positive samples. Median filter pre-processing came fourth. This method was particularly affected by false positives. If the gain is set at 20 instead of 25, its TPR equals that of the wavelet pre-processing, but with a FPR of 0.2. Nevertheless, analysis of the negative samples that produce some of these false positives show strong ‘pops’ in the recording (see for instance Fig. 12), which are probably caused by water drops hitting the microphone and generating an impulsive sound. An acoustic protection on the microphone could thus increase the TPR while decreasing the FPR. Anyway, it is remarkable that the correlation and the wavelet algorithms are not fooled by these pops. The fourth method, which consists on just taking the absolute value of the signal, outperformed the TEO operator not only in its TPR but also in its FPR, which coincides with Obeid and Wolf observations that included even more refined versions of the latter method [13]. As in the median filter case, the pops’ effect in the negative samples is present in both methods, which means that a similar protection of the microphone may increase their performance. Not considering, for instance, the negative sample of the water stream, brings the FPR down to 0.07 in the absolute value pre-processing, the same as in the second case of the wavelet method. No pre-processing, as 0.1 1500 0.7 0.6 5000 0.05 1000 0.5 TABLE I −0.05 0.6 0.5 0.4 0.3 Time(seconds) Running Average Energy coeffs 0.4 B EST (TPR, FPR) PAIRS , AT 0◦ , 90◦ , 180◦ 0 500 0.3 A LGORITHM R ANKING 0.05 0 0.2 0.1 False Positive Rate 0.5 0.2 Gain= 15 Gain= 20 Gain= 25 Gain= 30 Gain= 35 0 0 Binary detection, levels 4,5,6 0.1 0.4 0.3 0.1 1 500 0.6 0.5 0.2 Detection is evaluated for different gains. An example of such evaluation is shown in Fig. 10 for the wavelet algorithm. With the results from the evaluation of the 45 positive samples, plus the 15 negative samples, ROCs were plotted for each method. An example of such plots is given in Fig. 11. Table I shows the ranking of the best pairs for each tested method, with the corresponding gain for the threshold unit (C). 0 0.7 53 IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply. Proceedings of the Argentine School of Micro-Nanoelectronics, Technology and Applications 2008 Preprocessing Median: Stream 2 Binary detection 1 0.8 0.6 0.4 0.2 0 5 10 20 15 time (seconds) Signal: Stream 2 Gain=20 25 30 35 5 10 20 15 time (seconds) 25 30 35 0.4 0.2 0 −0.2 −0.4 −0.6 Fig. 12. False positive using median filter on a water stream recording. Notice the pop in the sample that fools the algorithm. A higher gain in the threshold detector circumvents the false positive, at the expense of losing some true positives. An acoustic protection on the microphone may be a simple solution for this false positive, without sacrificing the TPR. expected, gave the metric’s floor. Surprisingly, even no-preprocessing yielded better FPR results than the TEO operator. V. C ONCLUSIONS Detection of impulsive signals can be implemented with a wide variety of effective algorithms. A ROC statistical metric has been proposed in order to sort them in terms of detection efficiency and from the results obtained, some annotations have been given about their feasibility of VLSI integration. Clearly, correlation and wavelet-based detection algorithms give high performance at a higher hardware cost, but there exist good mixed signal approaches to their VLSI implementation. A median filter approach may be as hardware costly as the preceding methods, with inferior results. For that matter, just considering the absolute value of the signal, with a protected microphone, can offer a similar performance at a much lower hardware cost. ACKNOWLEDGMENT A. Chacón-Rodrı́guez is on leave from the Instituto Tecnológico de Costa Rica, on a scholarship funded by this institution and the Ministry of Science and Technology from Costa Rica. The authors thank Néstor Hernández Hostaller and Pablo Alvarado at the School of Electronics Engineering, Instituto Tecnológico de Costa Rica, for the high quality signal samples used in this case study. This work is funded by Project ANPCyT-PICT 2006 No. 1835, Project PGI-UNS 2006 No. 24/ZK17, and Project PIP 2005-2006 No. 5048 of CONICET. R EFERENCES [1] R. C. Maher, “Modeling and Signal Processing of Acoustic Gunshot Recordings, ” in Proc. IEEE Signal Processing Society 12th DSP Workshop, September 2006, p.p. 257-261. [2] P. G. Weissler and M. T. Kobal, “Noise of police firearms,” Journal of the Acoustic Society of America, vol. 56, no. 5, pp. 1515-1522, Nov. 1974. [3] R. Stoughton, “Measurements of small-caliber ballistic shock waves in air,” Journal of the Acoustic Society of America, vol. 102, no. 2, pt.1, pp. 781-787, Aug. 1997. ISBN 978-987-655-003-1 EAMTA 2008 54 [4] L. Green Mazerolle, C. Watkins, D. Rogan, and J. Frank, “Random Gunfire Problems and Gunshot Detection Systems,” in National Institute of Justice: Research in Brief, U.S. Department of Justice, Office of Justice Programs, National Institute of Justice, http://www.ojp.usdoj. gov/nij, Dec. 1999. [5] A. Dufaux, L. Bésacier, M. Ansorge, and M. Pellandini, “Automatic Sound Detection and Recognitions for Noisy Environment,” in In Proc. of the X European Signal Processing Conference, EUSIPCO 2000, http: //citeseer.ist.psu.edu/besacier00automatic.html, 2000. [6] K. Molnár, Á. Lédeczi, L. Sujbert, G. Péceli, “Muzzle Blast Detection Via Short Time Fourier Transform,” 12th MiniSymposium 2005 of the Department of Measurement and Information Systems, Budapest University of Technology and Economics, http://home.mit.bme. hu/˜kmolnar/index.html, 2005. [7] B. M. Sadler, L. C. Sadler and T. Pham, “Optimal and Robust Shockwave detection and estimation,” in Proc. 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’97), vol. 3, pp. 1889-1892, 1997. [8] B. G. Ferguson, L. G. Criswick, and K. W. Lo, “Locating far-field impulsive sound sources in air by triangulation,” Journal of the Acoustic Society of America, vol. 111, no. 1, pt. 1, Jan. 2002. [9] G.L. Duckworth, J.E. Barger, S.H. Carlson, D.C. Gilbert, M.L. Knack, J. Korn and R.J. Mullen, “Fixed and wearable acoustic counter-sniper systems for law enforcement,” in Proc. SPIE International Symposium on Enabling Technologies for Law Enforcement and Security Sensors, C3I, Information, and Training Technologies for Law Enforcement, November 1998, pp. 3575-3577. [10] Á. Lédeczi, P. Völgyesi, M. Maróti, G. Simon, G. Balogh, A. Nádas, B. Kusy, S. Dóra and G. Pap. “Multiple Simultaneous Acoustic Source Localization in Urban Terrain,” in Proc. Fourth International Symposium on Information Processing in Sensor Networks, IPSN 2005, April 2005, pp. 491-497. [11] M. Zu, P. Su, R. Shi, W. Wang, and J. Yu, “AntiHunter. Intelligent Tracer of Hunting Activities,” Lily Studio, University of Nanjing, June 2006. [12] A. I. Tarrero Fernández, Propagación del sonido en bosques. Análisis comparativo de las medidas in situ, en laboratorio y de los valores predichos por un modelo, Doctoral dissertation, Facultad de Ciencias, Universidad de Valladolid, 2002. [13] I. Obeid, and P. D. Wolf, P. D, “Evaluation of Spike-Detection Algorithms for a Brain Machine Interface Application,” IEEE Transactions on Biomedical Engineering, vol. 51, no. 6, pp. 905-911, 2004. [14] D. Heeger. “Signal Detection Theory,” http://www.cns.nyu. edu/˜david/handouts/sdt/sdt.html, 1997. [15] C. H. Hansen, “Fundamentals of Acoustics,” Department of Mechanical Engineering, University of Adelaide. www.who.int/ occupational_health/publications/noise1.pdf. [16] A. Dı́az-Sánchez, J. Ramı́rez-Angulo, A. Lopez-Martin, and E. SánchezSinencio, “A Fully Parallel CMOS Analog Median Filter”, IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 51, no. 3, pp.116123, March 2004. [17] I. E. Opris, and G. T. A. Kovacs, “A High-Speed Median Circuit,”, IEEE Journal of Solid-State Circuits, vol. 32, no. 6, pp. 905-908, June 1997. [18] R. T. Edwards, and G. Cauwenberghs, “Mixed-Mode Correlator for Micropower Acoustic Transient Classification,” IEEE Journal of SolidState Circuits, vol. 34, no. 10, p.p. 1367-1372, Oct. 1999. [19] S. Mukhopadhyay, and G. C. Ray, “A New Interpretation of Nonlinear Energy Operator and Its Efficacy in Spike Detection,” IEEE Transactions on Biomedical Engineering, vol. 45, no. 2, pp. 180-187, Feb. 1998. [20] T. Kaiser, et al, “Spatial aspects of UWB,” in UWB Communication Systems, ed. M. G. Di Benedetto et al, New York: Hindawi, 2006, ch. 5, pp. 253-410. [21] D. Goldberg, A. G. Andreou, P. Julián, P. O. Pouliquen, L. Riddle, and R. “VLSI Implementation of an Energy-Aware Wake-Up Detector for an Acoustic Surveillance Sensor Network.” ACM Transactions on Sensor Networks, vol. 2, no. 4, pp. 594-611, 2006. [22] D. Istrate, E. Castelli, M. Vacher, L. Besacier, and J. F. Serignat,“Information Extraction from Sound for Medical Telemonitoring,” IEEE Transactions on Information Technology in Biomedicine, vol. 10, no. 2, pp. 264-274, Apr. 2006. [23] A. Bultheel, Wavelets with Applications in Signal and Image Processing, http://www.cs.kuleuven.be/˜ade/WWW/WAVE/contents. html, 2008. IEEE Catalog number CFP0854E Authorized licensed use limited to: UNIVERSIDAD SUR. Downloaded on July 7, 2009 at 11:06 from IEEE Xplore. Restrictions apply.