Journal of Scientific & Industrial Research Vol. 73, Deceber 214, pp. 756-762 Coparison of Fourier Bessel (FB) and EMD-FB Based Noise Reoval Techniques for Underwater Acoustic Signals V Vijaya Baskar*, B Abhishek and E Logashanuga Faculty of Electrical and Electronics, Sathyabaa University, Chennai, India Received 6 August 212; revised 5 Noveber 213; accepted 29 Septeber 214 The purpose of this paper is to copare the efficacy of two algoriths used for denoising underwater acoustic signals affected by abient noise. The two denoising techniques are, (i) Fourier Bessel (FB) expansion based denoising algorith and (ii) Epirical Mode Decoposition (EMD)-Fourier Bessel (FB) based denoising algorith. Sea water norally contains unwanted background noise called abient noise which is non-stationary produced by an-ade or natural sources. In practical applications it is absolutely necessary to denoise underwater acoustic signals. The inforation that will be received through hydrophones shall be unaffected, pristine and original. In this paper, initially the two techniques are applied to a stationary input and the outcoes of both the techniques are copared. Later the two ethods are once again applied to anon-stationary input and the results are then copared. Keywords: Epirical Mode Decoposition, Fourier Bessel, Under Water Acoustic Signal, Abient Noise, Denoising Introduction Analyzing the inforation received is crucial in practical applications. The data transitted ay be non-stationary in nature and ay be stationary with only ono-coponent frequency or soeties ulti coponent frequencies. These days the counication through water is considered to be the ost unanageable ode of counication. Analyzing the signals is one of the popular fields of challenge in signal processing. Progress in underwater applications accelerates the research interest on underwater acoustic counications 3.Low frequencies suit best for underwater acoustic transissions and receptions. Usually natural noise gets added to a signal whenever it is transitted through a ediu of counication. It is an unwanted sound or a disturbance that gets naturally added to the original signal in the ocean consequently alters the original essage. Abient noise gets autoatically added to the acoustic signal when it is transitted through water as its ediu. Abient noise is the sustained unwanted background noise prevailing at soe spots in the ocean. It includes oentary sounds, like the noise of proxiity of ships and the occasional sounds caused by rain fall. It depends on the location, the depth at which the hydrophone is placed in the ocean to detect or receive *Author for Correspondence E-ail: v_vijaybaskar@yahoo.co.in signal fro subarine or the echo fro the target. Abient noise also includes the noise created by the hydrophone itself during its function and it even includes the electrical noises as well 11.Shipping noise can generate both teporal as well as spatial variability. The seasonal activities like fishing fleet cause teporal variability and the casual shipping routes cause the spatial variability. At a particular spot in an ocean the arine biological acoustic signals which are typically present today ay not be present toorrow and ay exhibit diverse spatial and spectral distributions. Sources of abient noise include plants and anials like fishes, Dolphins, whales etc., which are the ajor contributors of noise; even though plants in the arine ay not produce frequencies but they ay attenuate the signals. Noise produced by wind is yet another ajor source of the total abient noise. Wind associated abient noise was predicted and analyzed earlier by any researchers. Abient noise of wind depends on the varying wind speeds over the frequency range of 5 Hz to 5 KHz 11. In this paper two techniques viz. Fourier Bessel expansion based algorith and Epirical Mode Decoposition-Fourier Bessel based algorith available for denoising underwater acoustic signals are best copared for their efficacy and based on their coparative results the best suitable technique for various stationary and non-stationary inputs would be deterined.
BASKAR et al: COMPARISON OF FB AND EMD-FB BASED NOISE REMOVAL 757 Fourier Bessel Expansion Based Algorith The Fourier Transfor is not uch suitable for analyzing the non-stationary signals. Norally Fourier Bessel is used in place of Fourier Transfor for representing the signal in frequency doain. Fourier Bessel Expansion is proved to be natural choice for representing naturally occurring nonstationary signals. Fourier series coefficients are unique for a given signal in as uch as the sae way the Fourier Bessel coefficients are also unique for a given signal. Fourier Bessel functions are aperiodic and decay over tie unlike the sinusoidal basis functions in the Fourier transfor 5.In case of non-stationary signals, aperiodic signal set ay be ore efficient for representation. Fourier Bessel eploys these features which differentiate it fro Fourier Transfor and ake FB expansion ore suitable for analyzing non-stationary signals 2. In this paper zero-order Bessel function is chosen for the representation of non-stationary signals. The zero order Fourier Bessel expansion of a signal x(t) considered over an arbitrary interval (, s) is represented here-upon 2 Q x( t) C Where 1 J s t (1), = 1, 2, 3... are the ascending order positive roots of J =. J t are the zero s order Bessel functions. Considering the orthogonal nature of set J t, the Fourier Bessel coefficients C are s coputed using the following equation C s 2t x( t) a 2 J 2 J t dt a (2) With 1 Q, where Q is the order of the FB expansion, the J1 are the first order Bessel functions. The FB expansion order Q ust be known in advance. The intervals between the consecutive zero-crossings grow gradually with tie and reach π in the liit. In order to cover the full signal bandwidth the half of the sapling frequency, Q, ust be equal to the length of the signal if Q is unknown in advance 6. The Fourier Bessel Coefficient C for a signal x (t) = cos(ωt) achieves the peak value for the order where the root a.mean frequency is used to find the coefficients with highest agnitude. The window size should be selected in optiu to obtain good resolution. A larger window provides a finer resolution in frequency 7,8. It eans, to cover the sae signal bandwidth, ore nuber of Fourier Bessel coefficients will be needed. The bandwidth ay not provide enough entropy over the spread of frequencies due to change in aplitude. Mean frequencies were averaged for the given signal. They represent the centroid of the spectru and thus characterize the frequency coponents of noisy Signal. The algorith for denoising of underwater acoustic signal affected by abient noise using Fourier Bessel expansion based algorith is given below. 1. Siulated input signal is added with real tie wind noise signal. 2. The noisy signal is applied as input to the FB based denoising algorith. 3. Input signal is reconstructed fro the noisy signal. Epirical Mode Decoposition-Fourier Bessel Based Algorith Epirical Mode Decoposition is a signal processing technique aied to extract all the oscillatory odes ebedded in a signal. This decoposes a tie series data into coponents with well-defined instantaneous frequency. This procedure identifies the physical tie scales intrinsic to the data which is the tie interval between the successive axia and inia. Then each Characteristic Oscillatory ode is extracted which is called the Intrinsic Mode Functions 1,4. Each IMF contains varied frequencies. EMD ethod is an adaptive signal processing ethod which is very suitable for nonlinear and non-stationary signals. The original signal X (t) can be coposed by n order IMF and n X ( t) d ( t) r ( t) (3) i1 i n Where d i t are the intrinsic ode functions and r n t the residue 1.
758 J SCI IND RES VOL 73 DECEMBER 214 The algorith for denoising of underwater acoustic signal affected by abient noise using Epirical Mode Decoposition-Fourier Bessel is given below 1. Noisy signal is generated by adding input signal and real tie wind noise signal. 2. EMD is applied to the noisy signal, which is decoposed in to IMFs. 3. Since first IMF contain high frequency noise coponent, it is eliinated. 4. Denoised signal is obtained by adding all the IMF except the first one. 5. FB is applied to the denoised signal to iprove it further. First of all EMD is applied to the received signal which reoves all ajor noise frequency coponents and then the ean frequency of the signal is found out based on Fourier Bessel for analyzing the signal. Denoising algorith for stationary input signal Here a stationary sinusoidal signal of 5Hz is considered as input signal, which is then cobined with the wind noise to for noisy signal. The input signal is again retrieved out of the noisy signal using the Fourier Bessel expansion algorith. Figure 1(a) shows the input sinusoidal signal. The real tie wind noise signal, which is collected fro the ocean at 5.6 /s using a high sensitive hydrophone, as shown in the figure 1(b). The pure sinusoidal signal and the noise saples cobined to for a noisy signal are shown in figure 1(c).The noise signal i.e. the output of Fig. 1Input and output signals of FB based algorith
BASKAR et al: COMPARISON OF FB AND EMD-FB BASED NOISE REMOVAL 759 the hydrophone is a voltage signal. The input and the noise saples are converted into acoustic pressure on the sensitivity of the hydrophone 11. Fourier Bessel Expansion Based denoising Algorith Here the noisy signal is non-stationary in nature and can be analyzed using any ethods. Fourier series is one of the popular and efficient ethods for analyzing stationary signals. But abient noise is a non-stationary signal and as such Fourier transfor ay not be suitable for analyzing non-stationary noisy signal. So here we introduce Fourier Bessel expansion for analyzing noisy signal. This is so because the Fourier Bessel expansion is uch suitable for analyzing non-stationary signals 9.When Fourier Bessel is applied on a noisy signal, various coefficients are generated. All the coefficients of Fourier Bessel generated are unique. The original noiseless signal is reconstructed by identifying and adding all the significant coefficients. The figure 1(d) shows the coefficients order against agnitude and shows two significant peaks. Using the ean frequency it is possible to deterine the nuber of peaks in the coefficients versus agnitude graph. Here there are two peaks in figure, which represent two different signals. A signal can be reconstructed by suation of all the coefficients of a peak. It is iportant to identify the significant peak to reconstruct the signal. Now considering the first peak and by suing all the coefficients within the range of that peak to get the denoised signal, which is shown in figure 1(e).Then reconstruction, is perfored by considering the second peak. The denoised signal, which is obtained by suation of all the coefficients within the range of the second peak is shown in figure 1(f).Observing the two reconstructed signals, it is concluded that the first peak contains significant signal coponents. The denoised signal is quite satisfactory. EMD-FB Based denoising Algorith In this algorith EMD is first applied to the noisy signal. It decoposes the signal into finite nuber of Intrinsic Mode Functions (IMFs) 12. The frequency resolution of EMD has a threshold. Below the threshold, the EMD cannot decopose the signal into coponents of varied frequencies. It picks out the highest frequency oscillation that reains in the signal. Thus each IMF contains a band of lower frequency coponents than the one extracted just before. The first IMF has the higher frequency coponents, which are norally considered as noise. Adding all the IMFs except the first one gives denoised signal that is shown in figure 2 (a). It still contains soe noise coponents and as such the result is not satisfactory. So it is necessary to add soe ore algorith to obtain the desired denoised signal. By applying Fourier Bessel on the above signal, several coefficients are brought forth. Here figure 2 (b) presents coefficient order Vs their agnitude plot. Fro the figure it is evident that there is only one peak and by adding up all the coefficients of that peak the input signal can be reconstructed. The advantage of EMD here is that it reoves the unwanted peak. So there is only one significant peak. The denoised signal obtained is presented in figure 2(c).The coparison of reconstructed signal with the input sinusoidal signal is presented in figure 2(d). It clearly shows that input and denoised signals are siilar. Denoising Algorith for Non-stationary Input Here a non-stationary chirp signal is considered as an input and it is cobined with the noise to for a noisy signal. The input signal has to be reconstructed fro the noisy signal using the Fourier Bessel expansion algorith. Figure 3 (a) shows the input non-stationary signal, which is to be cobined then with the noise saples (5.6 /s) collected fro the ocean using hydrophone. Here the sae noise signal, which was used in the previous algorith and was shown in figure 1 (b), is considered. The input chirp signal and the noise saples collected fro ocean are cobined to for the noisy signal that is shown in figure 3(b). Epirical Mode Decoposition Fourier Bessel Algorith The EMD is applied to the non-stationary noisy signal. It decoposes the signal into finite nuber of Intrinsic Mode Functions (IMFs). The denoised signal using EMD is obtained conventionally through the addition of all the IMFs except the first IMF. It is presented in figure 3 (c). It still contains noise coponents and hence not satisfactory. In order to iprove the denoised signal now the FB based denoising algorith, which was used earlier for stationary input signal, is now applied. The order Vs agnitude plot is shown in figure 3 (d). All the coefficient are added to obtain the denoised signal. The coparison between reconstructed signal and the
76 J SCI IND RES VOL 73 DECEMBER 214 Fig. 2Input and output signals of EMD- FB based algorith (Stationary Input Signal) input chirp signal is presented in figure 3 (e).it shows that the input and the denoised signal are not siilar. i.e the output resebles the input during the lower frequency level but deviates subsequently as the frequency increases. This is due to the eliination of the first IMF. Norally the first IMF will have high frequency coponents which will be considered as noise.but in the case of non-stationary chirp input, which contains both the high and the low frequency coponents, the first IMF cannot be deleted. So the EMD will not be suitable here. So to iprove the denoised signal FB alone to be used without an EMD. Fourier Bessel Expansion Based Algorith In this algorith FB is applied to the noisy signal, which was shown earlier in figure 3 (b).the figure 3 (f) shows the coefficients against agnitude. Since the input signal is non-stationary chirp signal, the signal gets spread over a wide range in the spectru. A signal can be reconstructed by suation of all the coefficients of a peak. Observing figure 1(c) and figure 3(f) it is evident that the noise is present at order 16 and it can be oitted. So the denoised signal is obtained by the suation of the coefficients fro order 1 to 14. The reconstructed signal using FB alone is shown in figure 3 (g).the coparison of reconstructed signal and the input chirp signal is presented in figure 3 (h).it clearly shows that the input and as well as the denoised signal are siilar. The qualitative results show that the FB based algorith perfors pretty well for all non-stationary input signals.
BASKAR et al: COMPARISON OF FB AND EMD-FB BASED NOISE REMOVAL 761 Fig. 3Input and output signals for EMD-FB and FB algoriths ( Non-Stationary Input)
762 J SCI IND RES VOL 73 DECEMBER 214 Conclusion This paper presents the coparison between the two techniques of denoising acoustic signal affected by abient noise. Firstly a stationary sinusoidal signal of frequency 5Hz is considered as an input and it is cobined with the abient noise saples collected fro the ocean using a hydrophone to obtain the noisy signal. Fourier Bessel based technique is used to denoise the noisy signal and it is accoplished quite successfully by getting the signal copletely denoised. But in this ethod identification of the significant peak is done by trial and error ethod. Later the EMD was used to eliinate the unwanted peaks. So the EMD_FB perfored well for all the stationary input signals. Later the sae algorith was applied for the chirp input signal. But due to the eliination of the first IMF soe high frequency signal coponents got corrupted. To surount this proble FB alone used to perfor denoising. In this ethod the right noise peak was identified and eliinated to obtain the denoised signal and the output was found ideal. These algoriths are tested for different wind noise signal and produces siilar kind of results. Acknowledgeent The authors gratefully acknowledge Dr. Ra Bilas Pachori, Associate Professor, Electrical Engineering, Indian Institute of Technology Indore, for his valuable support and guidance. References 1 Chagnollean I M & Baranniuk R G, Epirical ode decoposition based tie-frequency attributes, 69 th SEG Meeting, Houston, United States, Noveber 1999. 2 Schroeder J, Signal processing via Fourier Bessel series expansion, Digital Signal Process, 3 (1993) 112-124. 3 Stojanovic M, Recent advances in high rate under water acoustic counications, IEEE J Oceanic Eng, 21 (1996) 125-136. 4 Balocchi R., Menicucci D, Santarcangelo E, Sebastiani L, Geignani A, Ghelarducci B & Varanini M,Deriving therespiratory sinus arrhythia fro the heartbeat tie series usingepirical ode Decoposition, Qauntitative Bio, 1 (23) 1-12. 5 Bracewell R, The Fourier Transfor and its applications. McGraw-Hill, 2. 6 Pachori R B& Sircar, Speech analysis using Fourier Bessel expansion and discrete energy separation algorith, Proc IEEE Digital Signal Process workshop, Wyoing, USA, 423-428 (26). 7 Ra Bilas Pachori, Discriination between Ictal and Seizure-Free EEG signal using epirical ode decoposition, Research Lett in SignalProcess, 28, Article ID 29356 (28). 8 Pachori R B, Hewson D J, Duchene J& Snoussi H, Analysis of center of pressure signals using epirical ode of decoposition and Fourier Bessel expansion,proc of IEEE Tenon Con, Hyderabad, India, (28) 1-6. 9 Pachori R B& Sircar P, EEG signal analysis using FB expansion and second-order linear TVAR process, Signal process, 88 ( 28) 415-42. 1 Pachori R B & Sircar P,Analysis of ulticoponent AM-FM signals using FB-DESA ethod, Digital signal process, 2(21 42-62. 11 Vijaya baskar V & Rajendran V, Wind Dependence of Abient Noise in Shallow Water of Arabian Sea During Pre- Monsoon, Proc of IEEE Int Con RSTSCC-21, (21) 413-416. 12 Vijaya baskar V& Rajendran V, Algorith for Denoising of Underwater Acoustic Signal using Enseble Epirical Mode Decoposition, Int J of Adv in Electron Eng, 2 (211) 24-246.