A Snore Extraction Method from Mixed Sound for a Mobile Snore Recorder

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1 J Med Syst (2006) 30:91 99 DOI /s z RESEARCH PAPER A Snore Extraction Method from Mixed Sound for a Mobile Snore Recorder Vivek Nigam Roland Priemer Received: 28 June 2005 / Accepted: 22 July 2005 C Science+Business Media, Inc This paper presents a snore recorder that can separate snores from their delayed mixtures. This is useful to study the snore sounds of individuals when these sounds occur in a normal in-home sleeping environment, where two people are sleeping together and both produce sounds. Based on methods for blind source separation, we give a snore separator that solves the blind delayed source separation problem and provide a performance index to monitor its convergence. The separated snores can be analyzed to detect symptoms of sleep apnea prior to polysomnography or as a monitoring device after polysomnography has been performed. Experimental results show good performance of the snore separator. Keywords Obstructive sleep apnea. Snoring. Blind source separation Introduction Sleep Apnea Syndrome (SAS) is a common sleep disorder that affects 2% of females and 4% of males in the adult population [1]. SAS is associated with increased cardiovascular morbidity, including systemic and pulmonary hypertension, cardiac arrhythmias and ischemic heart disease [2]. Studies have shown increased mortality of SAS patients, mainly from cardiovascular causes. Furthermore, studies have also shown that SAS patients with excessive daytime sleepiness are prone to motor and work-related accidents. Obstructive Sleep Apnea (OSA) is the most common type of SAS, in V. Nigam ( ) R. Priemer Electrical and Computer Engineering Department, University of Illinois at Chicago, Chicago 60607, USA R. Priemer vnigam1@uic.edu which the upper airway of the human respiratory system involuntarily collapses during sleep [2]. Young et al. [3] have reported that 93% of females and 82% of males with moderate to severe SAS remain undiagnosed. The gold standard for diagnosing SAS is a full night Polysomnographic (PSG) recording, from which the apnea/hypoapnea index is computed [2]. However, high costs and long waiting lists for overnight PSG recordings in sleep clinics delay diagnosis and the treatment of SAS. Elderly and/or sick patients may find the PSG equipment too cumbersome, and may be reluctant to spend the night in the sleep laboratory. Moreover, PSG recordings might also be affected by environmental and instrumentation effects. Ambulatory sleep monitoring techniques do not provide an adequate solution for the need to screen large populations for sleep apnea [2]. In many cases where the attendance of a technician is required, the cost associated with home monitoring is not much different from the cost of laboratory recordings. Therefore, a lot of research has been devoted to screen patients for PSG recordings by performing in-home clinical studies [2]. These studies concentrate on fewer clinical data modalities like, oxygen saturation level in blood, breathing movements and sleeping habits, and recording respiratory sounds [2], to name a few. Recently, snore signals have been analyzed to detect symptoms of SAS. During snoring the airway collapses partially causing the soft tissues in the back of the throat to vibrate as air passes through the narrowed airway. Snoring can be classified into two categories: intermittent snoring and persistent snoring. Intermittent snoring does not affect the sufferer during each night of rest and, although it may be caused by OSA, intermittent snoring may be triggered or exacerbated by obesity, smoking, alcohol consumption or, late night eating [4]. Persistent snoring is more likely a symptom of OSA than intermittent snoring and causes the sufferer to endure repeated interrupted sleep patterns on a nightly basis.

2 92 J Med Syst (2006) 30:91 99 Thirty percent of patients who snore have OSA [5]. Habitual snoring is known to affect up to 20% of the population. The male to female ratio of snorers is 2:1 with the gap closing after menopause [6]. Women with high incidences of smoking and drinking are more prone to snoring [6]. With such an alarming increase in the number of snorers, it is not surprising to find couples where both partners are habitual snorers. The features that are commonly extracted from snore signals to detect symptoms of SAS are the snore sound intensity[7] or the peak frequency of the snore spectrum [8]. Successful diagnosis of SAS by analyzing the pseudoperiodicity of the snore sounds has also been reported [9]. However, a study of snoring habits is likely to be more successful if the subjects are sleeping in their natural environments than by themselves in the stressful environment of a clinical laboratory, with a multitude of sensors attached to them. Sleep disruption, sleep onset insomnia, and changes in typical sleep patterns can occasionally occur in patients when sleeping in an unfamiliar environment such as a sleep laboratory [7]. These factors favor an in-home recording of snores. However, in-home monitoring of snores, for a sleeping subject, might be distorted by sounds, like a snore or a wheeze, made by a sleeping partner, resulting in mixtures of sounds being recorded instead of a pure snore sound. When a subject sleeps by himself, at home, sleep talk (somniloquy) or chest wheeze might interfere with snore recording. Since snores contain much turbulence like speech, traditional signal processing techniques like spectral filtering or timesegmentation are not suitable for separating snores from their mixtures. In this paper, we give an algorithm suitable for a portable snore recorder that can separate the snore, of a sleeping subject, from all the above-mentioned interferences. The snore recorder is particularly useful in cases were both the sleeping partners snore, creating the necessity of extracting the individual snores efficiently, in order to look for the symptoms of SAS. The algorithm removes the restriction of the subjects sleeping by themselves, thereby providing the most favorable sleeping ambience. We give a Blind Delayed Source Separation (BDSS) algorithm to estimate the snore of a subject from observed mixtures by assuming that the snore signals from the sleeping subjects are statistically independent of each other and of all other interfering sounds over time. Existing algorithms in the field of instantaneous Blind Source Separation (BSS) have not been successfully applied to separate snores from their mixtures due to the delays involved in the recording scenario and due to the absence of a generalized mixing model that accounts for the different sleeping configurations arising from movements of the sleeping subjects. This paper is organized as follows: Section 2 discusses the BDSS algorithm in detail and provides a solution to different mixing models that can arise from different sleeping configurations. Section 3 defines a performance measure for observing the convergence properties of the BDSS system. Section 4 discusses experimental results and Section 5 concludes the paper. Blind delayed source separation The three main hypotheses that make the delayed source separation of snores of the sleeping subjects possible are: (1) the sound from each sleeping subject is generated by independent physiological systems, and is therefore statistically independent from the sounds produced by other sleeping subjects; (2) the snores exhibit non-gaussian distributions that makes the application of BSS techniques possible; and (3) the snores generated by the sleeping subjects undergo some delay before mixing at the sensors. While hypothesis 1 follows from intuition, a histogram analysis of a snore signal verifies hypothesis 2. Figure 1 shows the density profile of a snore, demonstrating its approximately super-gaussian nature. Hypothesis 3 is necessary due to the speed of sound in air, assumed to be 330 m/s in this paper, and the distances between sound sources and sensors in a normal in-home environment. However, an instantaneous mixing model is not sufficient to account for the third hypothesis. A delayed mixing model, where each source experiences a delay before mixing with the other sources at the sensors is more appropriate to take into account sound propagation delays. Such a mixing model for two source mixing is given by x 1 (t) = a 11 s 1 (t d 11 ) + a 12 s 2 (t d 12 ) x 2 (t) = a 21 s 1 (t d 21 ) + a 22 s 2 (t d 22 ) (1) For the current problem, a ik is the attenuation incurred by the kth snore, s k, to reach the ith sensor, d ik is the propagation delay of the kth snore to the ith sensor, and x i denotes the observation made by the ith sensor. A common sleeping configuration, in which the snores might be recorded, is shown in Fig. 2. In this configuration, snore detectors, placed near the sleeping subjects, record a mixture of snores coming from both subjects. However, we must expect that the sleeping subjects do not remain stationary and move around while sleeping. Due to the movements by the sleeping subjects, another position that can occur is shown in Fig. 3.The snore recorder must be able to efficiently separate the snores from the mixtures arising out of all sleeping configurations. Torkkola[10] provided a solution for the model in Eq. (1) by assuming that d 11 <d 21 and d 22 <d 12, which gives rise to the following mixing model x 1 (t) = a 11 s 1 (t) + a 12 s 2 (t d 12 ) x 2 (t) = a 21 s 1 (t d 21 ) + a 22 s 2 (t) (2)

3 J Med Syst (2006) 30: Fig. 1. Histogram of a snore. Although this mixing model applies to the sleeping configuration shown in Fig. 2, it cannot represent the sleeping configuration shown in Fig. 3. There are a few features to be noted about the model in Eq. (1). First we do not associate any specific sensor with a sleeping subject, which is required in Eq. (2), where it is assumed that s 1, that represents the snore produced by subject 1, is the closest to sensor 1 that provides recording x 1. Thus, the propagation delay incurred by s 1 to reach sensor 1 is less than the time taken by s 1 to reach sensor 2 that provides recording x 2. Hence, the time of arrival of s 1 at sensor 1 is set as the time origin for s 1. In many practical problems, where the positions of the sleeping subjects are not known before hand, assigning a particular sensor to a particular source is not possible. We show this in Table I, where we have considered various recording situations and the associated mixing models. Note that the delays in the second column are the absolute delays, whereas the delays in the third column are the differential delays that are defined in Eq. (3). We notice that the recording scenarios in Case 1 (Case 3) and Case 2 (Case 4) are sufficient to represent the mixing of snores in the sleep configurations shown in Figs. 2 and 3, respectively. Since the delayed mixing model in Eq. (1) considers all of the possible recording scenarios, we call it the generalized mixing model for BDSS problems. To separate the sources Fig. 2. A common sleeping configuration corresponding to Case 1 and Case 3 (all distances are measured in cm). Fig. 3. A common sleeping configuration corresponding to Case 2 and Case 4 (all distances are measured in cm).

4 94 J Med Syst (2006) 30:91 99 from mixtures modeled by Eq. (1), we introduce differential delays and recover delayed versions of the original sources. The network used to separate the sources is shown in Fig. 4. If we define the differential delays as b 21 = d 21 d 11, b 12 = d 12 d 22 (3) then the network in Fig. 4, computes the u i (t), given by u 1 (t) = w 1 x 1 (t) + w 12 u 2 (t (d 12 d 22 )) + w 01 u 2 (t) = w 2 x 2 (t) + w 21 u 1 (t (d 21 d 11 )) + w 02 (4) which are the inputs to the nonlinearities defined by y 1 (t) = g(u 1 (t)) = (1/(1 + exp( u 1 (t))) y 2 (t) = g(u 2 (t)) = (1/(1 + exp( u 2 (t))) (5) We notice that the models arising out of Case 2 and Case 4 cannot be solved by using techniques given by Torkkola [10], because at least one of the differential delays in these models is negative. In the Section Different Cases Arising Out of the Generalized Mixing Model we provide an algorithm to solve Case 2 (Case 4). From Bell and Sejnowski [11], we know that minimizing the mutual information between the outputs y 1 and y 2 is equivalent to maximizing the entropy at the outputs, which is equivalent to maximizing E[ln J ], where J is the Jacobian of the network and E denotes the expectation operator. The adaptation rule for each of the parameters of the network can be obtained by calculating the gradient of ln J with respect to that parameter, and this is given by[12] w i (t) (1 2y i (t))x i (t) + 1/w i (t), i = 1, 2 (6) w 0i (t) (1 2y i (t)), i = 1, 2 (7) w ij (t) (1 2y i (t))u j (t b ij (t)), Table I. Delays options Case 1 Case 2 Case 3 Case 4 Different Recording Scenarios. Recording scenarios Resulting mixing model x 1 (t) = a 11 s 1 (t) + a 12 s 2 (t b 12 ) x 1 (t) = a 11 s 1 (t) + a 12 s 2 (t b 12 ) x 1 (t) = a 11 s 1 (t) + a 12 s 2 (t + b 12 ) d 11 < d 21 d 22 < d 12 x 2 (t) = a 21 s 1 (t b 21 ) + a 22 s 2 (t) d 11 > d 21 d 22 < d 12 x 2 (t) = a 21 s 1 (t + b 21 ) + a 22 s 2 (t) d 11 > d 21 x 1 (t) = a 11 s 1 (t b 21 ) + a 12 s 2 (t) d 22 > d 12 x 2 (t) = a 21 s 1 (t) + a 22 s 2 (t b 12 ) d 11 < d 21 d 22 > d 12 x 2 (t) = a 21 s 1 (t b 21 ) + a 22 s 2 (t) i, j = 1, 2, j i (8) The adaptation rules for the differential delays, b ij,are determined by b ij (t) (1 2y i (t))w ij (t) u j (t b ij (t)), i, j = 1, 2, j i (9) where we use the approximation u(t) = (u(t) u(t T ))/T (10) and where T is the sampling time increment. With Eq. (6) (10), the method of steepest ascent can be applied to the BDSS problem. These results are extendable for separating any number of sources by using b ij =d ij d jj, which is the differential delay that removes the interference of the source estimate u j from u i. Note that the differential delays must be positive for the BDSS algorithm to work properly. Otherwise, a source estimate u j will depend on a future estimate of another source u i. Different cases arising out of the generalized mixing model We now consider separately each case arising out of the generalized mixing model, and we give a method to use them. Case 1 and Case 3 (Table I): The differential delays in these mixing models are positive and the BDSS algorithm in Eq. (6) (10) can estimate the original independent sources. A subtle difference between Case 1 and Case 3 is that while in Case 1, u 1 (t) and u 2 (t) (in Fig. 4) are the delayed versions of s 1 (t) and s 2 (t), respectively; in Case 3, u 1 (t) and u 2 (t) (in Fig. 4) are the delayed versions of s 2 (t) and s 1 (t), respectively. Case 2 and Case 4 (Table I): One of the differential delays in these mixing models, b 21 in Case 2 and b 12 in Case 4, is negative and the algorithm in Eq. (6) (10) will fail to separate the sources. Therefore, we preprocess the incoming mixtures to make the differential delays positive before estimating the original sources. Consider the model in Case 4, i.e. x 1 (t) = a 11 s 1 (t) + a 12 s 2 (t) x 2 (t) = a 21 s 1 (t d 21 ) + a 22 s 2 (t d 22 ) (11) Delaying x 1 (t) byc seconds will yield the following mixing model: x 1 (t c) = a 11 s 1 (t c) + a 12 s 2 (t c) x 2 (t) = a 21 s 1 (t d 21 ) + a 22 s 2 (t d 22 ) (12)

5 J Med Syst (2006) 30: Fig. 4. The BDSS network to estimate original snores; where w denotes the weights, b the differential delays, and u the estimates of snores, s 1 and s 2. If we obtain u 1 and u 2 (in Fig. 4) as delayed and scaled estimates of s 1 and s 2, respectively, then b 21 = d 21 c b 12 = c d 22 (13) For the differential delays to be positive we require that } d 21 c 0 d 22 c d 21 (14) c d 22 0 When the condition given in Eq. (14) is satisfied, we estimate the original sources correctly. Now assume that the estimates u 1 and u 2 obtained in Fig. 4 are the delayed and scaled estimates of s 2 and s 1, respectively. Then we have b 21 = c d 21 b 12 = d 22 c (15) Again, for positive differential delays we require that } d 22 c 0 d 21 c d 22 (16) c d 21 0 Thus, the models in Case 2 and Case 4 can be used if c lies between the two delays in Eq. (12). However, we must address the following two problems to use the model in Eq. (12): 1. We must find a delay, c, that satisfies the conditions in Eq. (14) oreq.(16). 2. We must also determine which of the two mixtures, x 1 or x 2, is to be delayed by c seconds. Since at first we are only looking for an approximate estimate of the values of d 21 and d 22, we employ the crosscorrelation between x 1 and x 2 to estimate a value for c.however, more accurate techniques of estimating d 21 and d 22 in Eq. (12) can be found in Emile, Comon, and Leroux [13]. Analyzing the autocorrelations of x 1 and x 2 solves the second problem. The autocorrelations of x 1 and x 2 are given by r x1 (τ) = r s1 (τ) + r s2 (τ) r x2 (τ) = r s1 (τ + d 21 ) + r s2 (τ + d 22 ) (17) where τ is the time lag. Since r s1 (0) > r s1 (d 21 ) r s2 (0) > r s2 (d 22 ) (18) therefore, r x1 (0) > r x2 (0) (19) Therefore, we delay the mixture that has a larger autocorrelation value for zero lag. The algorithm for using Case 2 and Case 4 is described by the flow chart given in Fig. 5. Performance index for BDSS algorithms To define a performance index for BDSS algorithms, we give the steady state values of the cross-weights in the BDSS network. When the steady state values of u 1 and u 2 in Fig. 4 are the delayed estimates of s 1 and s 2, respectively, the steady state values of the cross-weights are given by w 12 = (a 12 w 1 /w 2 a 22 ) w 21 = (a 21 w 2 /w 1 a 11 ) (20) However, if the steady state values of u 1 and u 2 are the delayed estimates of s 2 and s 1, respectively, then the steady

6 96 J Med Syst (2006) 30:91 99 Fig. 5. Flow chart to solve the model in Case 2 (Case 4). state values of the cross-weights are given by w 12 = (a 11 w 1 /w 2 a 21 ) w 21 = (a 22 w 2 /w 1 a 12 ) (21) Currently, a performance index has not been proposed for monitoring the performance of BDSS algorithms, and the convergence of these algorithms is generally depicted by plotting separately the differential delay estimates and the cross-coupling weight estimates. This method becomes cumbersome with increasing complexity of the delayed mixing model in Eq. (1). For example, for a three source BDSS problem, six differential delays and six cross-coupling weights must be found. In such a situation, a global measure of convergence is desirable. Let us denote by ŵ i (t),ŵ ij (t), and ˆb ij (t) the estimates of w i (t), w ij (t), and b ij (t), respectively, that evolve over time towards the separating solution. Convergence of BDSS algorithms takes place in two phases. First, the differential delay estimates converge towards correct values, implying correct alignment of interfering signals from other channels. Then, the cross-weight estimates converge towards correct values in Eq. (20) or Eq.(21), subtracting the aligned interfering signals. Thus, in order to measure the performance of the BDSS algorithm, we use two performance indices to mea- Fig. 6. Convergence of differential delays (top) and cross-weights (bottom), for the mixing model in Eq. (31).

7 J Med Syst (2006) 30: sure convergence. For delay convergence, define a matrix of system differential delays as B ={b ij }, i j (22) where the ijth element is the actual differential delay, b ij, between the jth source and the ith sensor. Define another matrix, ˆB t,by ˆB t ={ˆb ij (t)}, i j (23) where the ijth element, ˆb ij (t), denotes the estimated value of the differential delay, b ij,afterthetth iteration of the BDSS algorithm. The diagonal entries of B and ˆB(t) are set to zero. Let B(t) = B ˆB t (24) Fig. 7. Snores, s 1 (top) ands 2 (bottom), used in the mixing model in Eq. (31). denote the differential delay estimation error between the actual differential delays and the estimated differential delays after the tth iteration of the BDSS algorithm. We give a performance index,pd 2 (t), for measuring convergence of the differential delays adaptation rule as P 2 d (t) = i j b ij 2 (t) (25) which is the Frobenius norm squared of B(t) and b ij (t)isthe ijth element of B(t). To monitor the convergence of the cross-weight estimates, we define a matrix C t by C t ={c ij (t)}, i j (26) whose elements are computed with c ij (t) = (a ij ŵ i (t))/(ŵ j (t)a jj ) (27) By constraining the elements of C t according to Eq. (27), we ensure that in steady state, when ŵ i (t)converges to w i, c ij (t) will represent the steady state values in Eq. (20). Let Ŵ (t) ={ŵ ij (t)}, i j (28) denote the matrix of estimated cross-weights after the tth iteration of the BDSS algorithm. The diagonal entries of C t and Ŵ (t) are set to zero. Let W (t) = C t Ŵ (t) (29) denote the difference between the cross-weight computed with Eq. (27) and the estimated cross-weights. We give a Fig. 8. The simulated mixtures, x 1 (top) andx 2 (bottom), in Eq. (31). performance index for measuring convergence of the crossweights adaptation rules as P 2 w (t) = i j w ij 2 (t) (30) which is the Frobenius norm squared of W (t), and w ij (t) is the ijth element of W (t). Therefore, our goal is to achieve the minimum ofp 2 d andp2 w. Experiments and results In order to evaluate the performance of the BDSS algorithm in estimating the snores from their mixtures, the sleeping configurations shown in Figs. 2 and 3 were simulated. Two snore signals, s 1 and s 2, one from a male and the other from a female, were recorded at a sampling frequency f s =22.05 KHz (T=1/f s =0.045 ms), and mixed according to

8 98 J Med Syst (2006) 30:91 99 Fig. 9. The estimated snores, u 1 (top)andu 2 (bottom), from mixtures in Eq. (31). the following mixing model: x 1 (t) = 0.06 s 1 (t 94T ) s 2 (t 107T ) x 2 (t) = 0.32 s 1 (t 42T ) s 2 (t 29T ) (31) This mixing model arises from the sleeping configuration shown in Fig. 3. In Eq. (31), s 1 is delayed by d 11 =94T=4.23 ms on reaching sensor recording x 1. Figure 6 shows the convergence of the differential delay estimates and the cross-weight estimates for the model in Eq. (31). Notice that both the differential delay estimates and the cross-weight estimates converge around 17 s from the initialization. Figure 7 shows the original snores that were mixed with Eq. (31) to generate the mixtures that are shown in Fig. 8. The esti- Fig. 11. Convergence of differential delays (top) and cross-weights (bottom), for the mixing model in Eq. (32). mated snores are shown in Fig. 9, where we note that around 17 s, the snores are satisfactorily separated from each other. The recording of snores is often corrupted by background noise such as air conditioning or ventilation noise. In order to test the robustness of the BDSS algorithm in the presence of such background noises, we simulated a situation where the snores were mixed according to the following mixing model x 1 (t) = 0.6 s 1 (t 29T ) s 2 (t 113T ) + n 1 (t) x 2 (t) = 0.05 s 1 (t 106T ) s 2 (t 24T ) + n 2 (t) (32) This mixing model corresponds to the sleeping configuration shown in Fig. 2. The additive noises n 1 (t) and n 2 (t) are different realizations of air conditioning noise that were downloaded. The SNR (signal to noise ratio) of the recorded mixtures was approximately: SNR=22 db. Mixtures with very low SNR can be denoised prior to the application of the BDSS algorithm [12]. No denoising was performed for the current experiment. Figure 10 shows the frequency spectrum of the air conditioning noise that was used in Eq. (32). Figure 11 shows the convergence of the differential delay estimates and the cross-weight estimates for the model in Eq. (32). Very often, sleeping subjects move, changing the values of the differential delays and the mixing coefficients, as well as the sleeping configuration. To study the performance of the BDSS algorithm for tracking nonstationary differential delays and cross-weights, we abruptly changed the model in Eq. (32) at time t=23 s to the following mixing model Fig. 10. (32). The frequency spectrum of the air conditioning noise in Eq. x 1 (t) = 0.05 s 1 (t 100T ) s 2 (t 115T ) + n 1 (t) x 2 (t) = 0.28 s 1 (t 50T ) s 2 (t 40T ) + n 2 (t) (33) Thus the mixing model changes from the one in Case 1 to the model in Case 2. Figure 12 shows the convergence of the differential delay estimates for the model in Eq. (32)

9 J Med Syst (2006) 30: Using a delayed sound mixing model, we have presented a snore recorder that can extract the individual snores of sleeping subjects from the observed snore mixtures. This enables physicians to monitor the snoring habit of each subject in a most natural sleeping environment without isolating subjects from each other. The separated snores can then be analyzed to detect symptoms of OSA. In addition to performing like a personal healthcare device, the snore recorder can also help a user to obtain preliminary results while the user waits for a full scale PSG. References Fig. 12. Tracking of differential delays in the presence of a nonstationarity when the mixing model in Eq. (32) changes to the one in Eq. (33) att=23 s. before and after the model parameters are changed. Notice that the differential delay estimates converge toward steady state values until at time t=23 s when the differential delays change due to the change in the mixing model. Then there is a jump in the performance index for the differential delays at time t=23 s. However, the BDSS algorithm tracks the changed values of the differential delays properly and by the time t=48 s, it is again operating in steady state. The cross-weights are also tracked in the samed way. To facilitate automatic switching between the models in Eq. (32) and (33), the condition in Eq. (19) was checked for N consecutive windows of the incoming mixtures, at regular intervals. If the condition in Eq. (19) was satisfied for all the N consecutive windows, a decision was made in favor of the model in Case 2 (Case 4), else it was assumed that mixing was taking place according to the mixing model in Case 1 (Case 3). For the current work, N was chosen to be N=100 and a window duration of 256T was used. Similarly, to track a mixing model change from Case 3 to Case 4, we run the algorithm in Fig. 5 in parallel to its other copy that tracks changes in mixing from Case 1 to Case 2. Conclusion 1. Available at: 2. Shochat et al., The SleepStripTM: An apnea screener for the early detection of sleep apnea syndrome. Eur. Respir. J. 19: , Young et al., The occurrence of sleep-disordered breathing among middle-aged adults. New Engl. J. Med. 328: , Available at: apnea snoring. htm. 5. Available at: Snoring SleepApnea.asp. 6. Available at: 7. Available at: articleid=s0209f Sola-Soler, J., Jane, R., Fiz, J. A., and Morera, J., Snoring sound intensity study with ambient and tracheal microphones, Proc. 23rd Annu. Int. Conf. IEEE, 2, Engineering in Medicine and Biology Society, pp , Sola-Soler, J., Jane, R., Fiz, J. A., and Morera, J., Pitch analysis in snoring signals from simple snorers and patients with obstructive sleep apnea, 24th Annu. Conf. Annu. Fall Meeting Biomed. Eng. Soc., EMBS/BMES Conf., Proc. 2nd Joint, 2, Engineering in Medicine and Biology Society, pp , Torkkola, K., Blind separation of delayed sources based on information maximization, Proc. IEEE ICASSP, 4, Atlanta, GA, pp , Bell, A. T., and Sejnowski, T. J., An Information maximization approach to blind separation and blind deconvolution. Neural Comput. 7(6): , Nigam, V., and Priemer, R., Blind delayed source separation, Electronic Proc. CITSA, Orlando, Emile, B., Comon, P., and Leroux, J., Estimation of time delays with fewer sensors than sources. IEEE Trans. Signal Process. 46(7): , Sola-Soler, J., Jane, R., Fiz, J. A., and Morera, J., Spectral envelope analysis in snoring signals from simple snorers and patients with Obstructive Sleep Apnea, Proc. 25th Annu. Int. Conf. IEEE, 3, Engineering in Medicine and Biology Society, pp , Haykin, S., Unsupervised adaptive filtering, Blind Source Separation, Vol. 1,Wiley Interscience, New York, NY, 2000.