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(8) . Biomedical Signal based on wavelet transform and AR model with Support Vector Machine for mobile biomedical signal Fan-Che Yen Department of Mechanical Engineering National Taiwan University Abstract This thesis describes the embedded system technology in the monitoring device for the National Taiwan University Wireless Health Advanced Monitoring Bio-Diagnosis System (WHAM-bios). The WHAM-bios consists of body-embedded sensors, a monitoring device, and a center health care server. A prototype of the monitoring device and the health care center is implemented in this thesis. The monitoring device is a smart phone running Symbian operating system. The biomedical diagnosis system is implemented in the center health care server as well as the smart phone. The thesis uses Electrocardiogram (ECG or EKG) as example. The ECG signal analysis is based on spectral estimation, wavelet transformation and principal component analysis. The diagnosis dealing with healthy state and six other arrhythmia abnormalities is based on support vector machine classification algorithm. Keywords: Biomedical Diagnosis System, Smart Phone, Spectral Estimation, Wavelet Transformation, Principal Component Analysis, Support Vector Machine, Electrocardiogram. . II.

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(10) . Chapter 1. Introduction .................................................................................................................. 1. 1-1 Motivation and Objective..................................................................................................... 1 1-2 Related Works ...................................................................................................................... 4 1-3 Organization of this thesis.................................................................................................... 9 1-4 Contributions........................................................................................................................ 9 Chapter 2. System Architecture and Environment ...................................................................... 13. 2-1 System Architecture ........................................................................................................... 13 2-2 Hardware Architecture ....................................................................................................... 14 2-3 Software Architecture ........................................................................................................ 15 2-3-1 User Interface ............................................................................................................. 16 2-3-2 Signal processing ....................................................................................................... 17 2-3-3 Data communication .................................................................................................. 17 2-3-4 Records of Daily Biomedical Signal .......................................................................... 23 Chapter 3. Signal Analysis Theorem ........................................................................................... 25. 3-1 Random Process ................................................................................................................. 25 3-2 Spectral Analysis................................................................................................................ 31 3-2-1 Classical Spectral Estimation ..................................................................................... 32 3-3 Wavelet Transformation .................................................................................................... 39 3-3-1 Fundamental Concept................................................................................................. 39 3-3-2 Multi-level Decomposition[32] .................................................................................. 41 3-3-3 Mother Wavelet .......................................................................................................... 43 3-4 Principal Component Analysis........................................................................................... 44 3-5 Support Vector Machine .................................................................................................... 45 3-5-1 Support Vector ........................................................................................................... 45 3-5-2 Lagrange’s multiplier ................................................................................................. 48 3-5-3 Feature Space and Kernel [33] ................................................................................... 50 3-5-4 Decision Function ...................................................................................................... 51 Chapter 4. System Implementation .............................................................................................. 53. 4-1 Hardware Implementation.................................................................................................. 53 4-2 Software Implementation ................................................................................................... 54 4-2-1 Socket/Bluetooth Connection..................................................................................... 55 . III.

(11) . 4-2-2 Mobile Database......................................................................................................... 57 4-2-3 User Interface ............................................................................................................. 57 4-2-4 Remote Server ............................................................................................................ 58 4-3 Signal Processing ............................................................................................................... 59 4-3-1 Basic Concept of ECG Signal .................................................................................... 60 4-3-2 Preprocessing of ECG Signal ..................................................................................... 63 4-3-3 Feature Extraction ...................................................................................................... 65 4-3-4 SVM Classification .................................................................................................... 67 4-3-5 Experimental Result ................................................................................................... 71 Chapter 5. Conclusions and Future Works .................................................................................. 77. 5-1 Conclusions ........................................................................................................................ 77 5-2 Future Works...................................................................................................................... 78 References. . . .................................................................................................................................... 79. . IV.

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(65) . Chapter 1 1-1. Introduction. Motivation and Objective According to the definition of "aging society" by United Nations, when the population of people. over 65 years old is more than seven percent, that society will be called "aging society". With this definition, Taiwan became a so-called “aging society” in 1993.[1] With the falling of birth rate and the rising of elderly population, the aging phenomenon of our composition of population will be very obvious and will still growing continuously. Therefore, the home care services become important and the demand would be largely rising. The number of nurses will not be enough for the large elderly population. In order to meet the demand, we design a health-care system to monitor the health conditions of old people or patients. In order to meet the demand, Taiwan’s Ministry of Economic Affairs supports the Nano-BioMEMS Group in National Taiwan University (NTU) to develop a “Wireless Health Advanced Monitoring Bio-Diagnosis System (WHAM-Bios)”[2]. The WHAM-Bios project aims to perform real-time C-Reaction Protein (CRP) detection in blood serum, because C-Reaction Protein is generally regarded as the indicator of heart disease detection and many other symptoms of disease. And the detection results from the sensor node would be sent to a health monitoring device through a miniature RF system. And the health monitoring device is responsible for collecting the detection results, doing preliminary analysis, and sending out data to doctors or health care center. This thesis is to design and implement the health monitoring device. To implement such a device, embedded system is chosen to be our core system because it can be customized to meet our requirements, such as small size and low power consumption. And Symbian OS is chosen to be the embedded operating system, which is commonly seen in mobile phone no matter it is a smart phone or not. . 1.

(66) . Besides developing the embedded system prototype, the signal analysis is also implemented in the system. The signal analysis is based on spectral estimation, wavelet transformation and Support Vector Machine theorem. Spectral estimation is one kind of theory that determines the spectral content of a random process which is a finite set of observations from the process. Because the biomedical signal can be regarded as a random signal, spectral estimation is chosen to be our analysis method. There are, in general, three types of randomness existing in biomedical signals: Measurement Randomness – This is most often a high frequency noise induced by the sensor electronics. Individual Randomness – Biomedical signals measured of different individuals always differ in various aspects. This is the difference due to their physical and mental conditions. Time Randomness – Biomedical signal characteristics change with time even if they are measured from the same person (time-varying system). This is because the characteristics presented in the signal stand for the states of the body at certain instances and the body states are easily affected by environment, physiological and psychological excitations. Among these kinds of randomness, the first random factor widely exists in mechanical, electrical, biological systems; and the two other random factors are special to the biomedical signals. As a result of these properties, it is difficult to characterize the biomedical signals with the common deterministic signal parameters like rise time, peak time, etc. Instead, statistical parameters like first order moments (means), second order moments (variances), and even the power spectrum densities become more suitable for the analysis. The WT (wavelet transformation) is a signal processing process that decomposes a signal into two parts, one is called high frequency part and the other is low frequency part. The most obvious usage is to de-noise no matter the polluted part is high frequency or low frequency. The frequency threshold can be done by selecting appropriate wavelet and number of decomposition level. The level is chosen so that the wavelet coefficient containing the certain frequency, say 60HZ, the electrical noise. There are many families of wavelets and it is usually choosing Daubenchies as the wavelet corresponding to ECG signal. Usually one will test different levels of wavelet families to . 2.

(67) . find out which of the levels is best suited to the certain type of signal, since different type of diseases gives different type of signal characteristics. Principal Component Analysis (PCA) is a mathematical way to identify patterns of data and to express the data in a way as to highlight similarities and differences among data. The advantage of PCA is that once we found patterns of data, and we can reduce the number of dimensions without much loss of the signal information (Of course, there’s a criteria of how many dimension we should keep). This technique used here is to reduce the feature combined with parametric model and wavelet transform to 3D because of two reasons. The first reason is that data in dimension higher than 3 cannot be plotted and unfortunately, human beings are living in a 3D world (In other words, we can’t separate different patterns of data visually if dimension is higher than 3D). The other reason is that the reduction of dimension also reduces the computation time of Support Vector Machine without losing much accuracy. This is particularly useful because this thesis is to be in the mobile phone with much slower computation speed than PCs do.[3] SVM (Support Vector Machine) is a branch of machine learning, and it is originally designed as a supervised machine learning algorithm.[4] It is the algorithm that does diagnosis to the biomedical signal in this thesis. Since MIT-BIH arrhythmia database is notated with different diseases by doctors, we can feed SVM with the notated input and thus result an output classifying the input into classes with different biomedical symptoms. However, sometimes the feature acquired from biomedical signal is hard to recognize in a relative low dimension. To classify those features that are ambiguous in low dimension, a method utilizing kernel function can be used to map inputs into higher dimension and construct a SVM model. Meanwhile, a database is also created. Used not only as storage but also as a basis of comparison, the database records daily biomedical signal of a patient. However, it won’t be receiving any signal from the mobile biomedical signal system. Instead, when the patient came home and plugged the mobile phone, it then records the signal for the sake of not wasting power . 3.

(68) . during outdoor time. The forgetting factor is applied to this database. Each time a signal comes in, it is marked with time stamp. The newest data is multiplied by forgetting factor 1 while the second newest is multiplied by 0.9. That means the third data is multiplied by 0.9 twice and so on. This is because biomedical signal varies as time goes. The classification model generated by old data is not always correct when a person’s health condition changes, such as getting fatter or being stressed because of outer environmental differences. Newer data owning greater influence on the model of SVM is the main idea of this database. In this thesis, electrocardiogram (ECG) is used as example to verify how these theorems are applied to the Bio-diagnostic category. We mainly aim at the arrhythmia symptom diagnosis with the ECG waveform not directly being applied in our analysis. Instead, the combination feature of parametric spectral estimation model and the wavelet de-noised signal is the input feature followed by PCA.. 1-2. Related Works There are extensive studies among ECG-based clinical applications. However, there are still. upcoming novel approaches of researches on this issue. We will provide a general review of the related works in this section. The WHAM-Bios is a health monitoring and diagnosis platform that provides a convenient communication between doctors and patients. The concept of building a health monitoring platform can be found in many researches. M-Health[5] is a similar system which is defined as “mobile computing, medical sensor, and communication technologies for health care”. The generic organization of the health monitoring system that conforms to the definition of m-Health is illustrated in Fig. 1-1. In this organization, a variety of sensors are attached to a human body in order to monitor the health condition of the patient. A gateway is responsible for acquiring the detection results from the sensor nodes and a wireless body area network is established for their . 4.

(69) . communication with Bluetooth[6] or ZigBee[7]. The gateway communicates with the remote monitoring server through Bluetooth or wireless LAN (WLAN) to upload the health information of the patient.. Fig. 1-1 A typical organization of the m-Health monitoring system[5] When it comes to the WHAM-Bios[2], the basic architecture is almost the same as the m-Health monitoring system. However, there are still some differences: the attached sensors in m-Health system become implanted in the human body in the WHAM-Bios. In order to lower the power consumption, RF technology is chosen to be our wireless body area network. And the gateway is developed with an ARM embedded system for the purpose of small-size and the specific use for the WHAM-Bios[8]. The embedded operating system in our embedded device is Windows CE developed by Microsoft Corporation. In [8], the author indicates the features and the advantages of Windows CE and the concept of the development environment. The communication between the gateway and the remote monitoring server is implemented with the WLAN because of the short range of Bluetooth. Another important feature of the WHAM-Bios is the diagnosis platform which . 5.

(70) . is based on the spectral estimation and fuzzy C-means clustering analysis. There are other researches on the ECG signal analysis with similar theorems. In [8] and [9], the wavelet analysis is applied to analyze the ECG signal by extracting the QRS complex feature. Wavelet analysis is mostly applied for the analysis of the signals that are non-continuous and have some sharp waves. The concept of wavelet analysis is very similar to Fourier analysis which is also a wave analysis. Fourier analysis expands signals or functions in terms of sinusoids which is extremely valuable in mathematics, science, and engineering, especially for periodic, time-invariant, or stationary phenomena. A wavelet is a “small wave”, which has its energy concentrated in time to give a tool for the analysis of transient, non-stationary, or time-varying phenomena. That is to say, the Wavelet analysis has the ability to allow simultaneously time and frequency analysis. This thesis proposes another analysis tool for biomedical signals – spectral estimation. Spectral estimation is also a popular analysis technique for biomedical signals which are regarded as random processes. It is not to deny the achievements of wavelet analysis on ECG signals, but to try another approach to ECG analysis and might be able to combine these two techniques to achieve a better result. The author uses the fuzzy C-means clustering analysis as the technique of diagnosis. In this thesis, fuzzy C-means clustering algorithm is also used to make preliminary diagnosis on the patient’s health condition. In [9], the set of features which is used in the fuzzy C-means clustering algorithm is extracted from the ECG waveform. They are the period, QRS complex time interval, RS wave time interval, ST wave time interval, the amplitude of QRS complex, and the amplitude of T wave. However, in this thesis, the AR parameters obtained from spectral estimation are used in the fuzzy C-means clustering algorithm. Since the appearance of SVM [10], there are many researches focusing on the use of SVM with other known algorithm playing the role of feature extraction/selection while there were sometimes used as classification methods. Terrence et al. [11] introduced an approach of combining SVM classifying two classes of cancer tissue. They use a dot-product kernel to map the feature. . 6.

(71) . Instead of SVM, they also use the ones based on the perceptron algorithm that generates almost the same result as SVM. However, this thesis is mainly focused on tissue recognition. It did provide a clear view of how to implement SVM. The author also concluded that more training and testing samples would increase the performance of SVM. Lena et al. [12] introduced a system of PCA related classification algorithm called SIMCA with its feature to be directly measured by SIEMENS Megacart. Biomedical signal measured is applied of correlation. The higher correlation between different leads of different features, the less likely to be used by the authors. That is because features like that tend to misclassified by SIMCA, also because they can reduce the amount of less important data and saving computational time. Total numbers of twenty classes are classified for 8 times. The author suggested that ECG measurement signal contains a lot of redundant information so the feature selection step is crucial to the successful rate of classification. Also, the conclusion that fewer numbers of features will increase the number of misclassified samples is observed. Stanislaw et al. [13] uses a database called MIT-BIH Arrhythmia Database [14]. A combination of multiple classifiers by weighted voting principal is proposed so that each classifier influences the final decision is based on the performance on training. The authors use the QRS complex of the ECG, proposing the description of it by higher order statistics and the Hermite basis functions expansion, as features inputting to SVM. Total numbers of thirty classes are taken into consideration with train sample number up to 6690 and test sample up to 6095. Using each classifier individually is less good than integration of these two classifiers, which is the result the authors presume. However, which kernel SVM used is not mentioned. Salim et al. [15]. proposed a method to classify patients prone to atrial fibrillation via SVM and a database selection of collaboration with Brest University Hospital. They only use P-wave delineation of sampling rate at 1KHz, which was bandpass filtered between 0.01 Hz and 40 Hz. Unlike any other feature extraction algorithm, the authors simply bandpass filtered them with the . 7.

(72) . knowledge of atrial fibrillation is most visible on P wave. Although the result was not so promising but it does save a lot of time computing, it is still a above average method. Digvijay et al. [16] proposed a method of classifying cardiac abnormalities with SVM of RBF kernel and a feature extraction algorithm of continuous wavelet transform (CWT). PTB Diagnostic ECG Database raw signals are preprocessed through FIR filter, and then extracted to be an 18dimension feature by means of CWT. 6 numbers of classes are taken into consideration. It shows really high accuracy up to 100% of classifying correctly. Hao et al. [17] introduced a method almost the same as above but to use PCA as feature extraction method and a classifier. Different classifiers are combined together to see if they can have the best performance. The authors also found out that it is not necessary to extract too many principal component since it increase dramatically the computation time. Four kinds of diseases from MIT-BIH arrhythmia database are considered then. únan et al. [18] combined discrete wavelet transform of different mother wavelet and the combined neural network model to classify ECG. They first calculate the wavelet-transformed features to statistical features, that is, mean of the absolute values of the coefficients of wavelet transform, average power of the wavelet coefficients, standard deviation of the coefficients and the ratio of the absolute mean values. This made the preprocessing procedure slightly complex but makes it efficiently generating model. According to the thesis, it showed a great result of classification accuracy. In the following year, the co-author of [18] Elif Derya hbeyli [19] used another classifier SVM with the error correcting output codes (ECOC) and the same feature extraction algorithm (remember statistical feature?) to classify four different types of abnormalities. Compared with MLPNN proposed in the thesis, SVM showed greater result of accuracy as well as CPU time. Elif later introduced different feature extraction algorithm along with neural network classification algorithm[20]. The author did compare a lot of method and give conclusions. That is, different algorithm possesses different characteristics and no one can say which one is better than others. . 8.

(73) . According to these theses, one thing is for sure. Various methods show different advantages and disadvantages. Even if the performance of certain algorithm is high against others, it may be weak on classifying, say, arrhythmia abnormalities. In this thesis, we are dealing with arrhythmia diseases. Combining autoregressive model, wavelet transform and principal component analysis as feature extraction method, SVM with RBF kernel is applied. Also, we use cross-validation and grid search of parameters to verify the performance of this classification method.. 1-3. Organization of this thesis The system architecture of the mobile biomedical signal analysis system is introduced in. chapter 2, including the hardware layer and software layer. In the first half of chapter 3, spectral estimation theorem, wavelet transformation and principal component analysis are introduced. While in the latter half of chapter 3, the classification theorem – support vector machine is introduced. In chapter 4, the implementation of the system is presented and is divided into two categories. First, the software and hardware implementation of our system is introduced, including the health care device and the server. Secondly, a novel approach to ECG signal analysis is presented. Finally, conclusions of this thesis and the future works of the system will be presented in Chapter 5.. 1-4. Contributions. Development of portable application of smart phone The use of mobile phone is skyrocketing high. The hardware of that is getting better. However, the lack of a well-designed application is common problem.. . 9.

(74) . We designed a Java based application. It monitors incoming biomedical signals, gives diagnosis to that and alarms when it detects abnormalities. Also, a neat user interface that displays all information works above all the undergoing functions of storing and analyzing, so that the users do not spend much time to be familiar with the annoying operation interface. The best of all, it is, as I stated, written in Java. That means we reduced the effort to rewrite/compile programs if different platform OSs are to use. Serial & socket communication development on embedded system Serial communication is the most basic communication tool for embedded system to receive or send out data because the protocol is simple. In this thesis, we communicate with the Bluetooth transceiver through the serial port, thus the development of serial communication becomes one of our key points. Network becomes the most popular tool of communication in Information Technology these days and network transmissions are actually based on the socket communication. In this thesis, we communicate with the remote health care center through networks, therefore the development of socket communication is also what we are focusing on. Apply spectral estimation, wavelet transformation, principal component analysis and support vector machine theorem to ECG signal analysis and diagnosis Since this is a bio-diagnosis platform, the mechanism of autonomous diagnosis should be built. This thesis proposes a novel approach to ECG signals diagnosis which combines spectral estimation, wavelet transformation, principal component analysis and support vector machine theorem. We offered a way of combining these well-known theorems and generated a good result. Integration and development of a prototype for an Autonomous Health Monitoring Platform The integration is always the most important part of developing an embedded system since the developers should be well familiar with every part of the system and know all the related knowledge . 10.

(75) . and techniques. In this thesis, we complete a prototype of the autonomous health monitoring platform, including a health monitoring device, a health care center server, and a built-in autonomous diagnosis platform. Our Integration with ECG, s100, CRP has successfully been completed. The socket communication to the server of remote hospital has been completed. Our Autonomous Health Monitoring Platform is now working well with wireless network functioning. Besides, a brand new idea called forgetting factor is applied. The forgetting factor is designed to fit a person’s physical characteristics to solve the uncertainty of daily physical changes, such as getting fatter. . . 11.

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(77) . Chapter 2. System Architecture and Environment. In this chapter, we will roughly introduce the architecture of the whole system, from the user-end to the server-end. And the mobile biomedical signal analysis system, which is our main focus of this thesis, will be introduced in more detail.. 2-1. System Architecture Fig. 2-1[21] illustrates our system architecture. Every cluster represents one single patient. The. sensor nodes are embedded in the human body and extract the useful data about the patient’s health condition. And then they will send the data to the mobile device, which is carried by the patient. The mobile device makes preliminary analyses when they receive enough data from the sensor nodes. Signals being processed, the mobile device will then send the data to the health care center if the biomedical signal is suggested illness by algorithm proposed in this thesis, where there are doctors or nurses who can make the final diagnosis. In the mean time, mobile biomedical signal analysis system also saves patient’s daily biomedical signal to database. There’s a forgetting factor controlling how important the data is. Older data is multiplied by a smaller factor and vice versa. Why so? Since biomedical signal differs from time to time for a single person, the model generated by algorithm used to distinguish normal and illness may be inappropriate. With this type of database introduced, we can diminish the effect of natural human reaction, such as getting fatter, being sensitive to outer environment…etc. Those situations would change a person’s normal definition thus creating a misleading judgment. And this is the novel idea of the mobile biomedical signal analysis system.. . 13.

(78) . Internet or satellite. Health Care Center. … Cluster. Mobile device. Sensor node. Fig. 2-1 System Architecture. 2-2. Hardware Architecture Various works have been done by researchers [22][23][24]. They choose to implement their. algorithm within a custom WinCE device for the purpose of installing any program they won’t to reduce the usage of memory and power consumption. However, such health monitoring devices without capability of communications are now not so suitable for this task. People who suffer from illness who need constantly health condition monitoring will have to carry a mobile phone and a health monitoring device simultaneously. Luckily, smart phone is now available for a low price (Well, thanks for the sky-rocketing high production). Usually, a smart phone is equipped with Bluetooth connection and wireless connection module not to mention the 3 and 3.5G connection module. We can use these modules as protocols to receive raw data and to send processed data. The layout would be as Fig. 2-2. . 14.

(79) . Bluetooth module is used to receiving data from sensor inside human body for the reason that it is almost available in every smart phone. As for security concern, Bluetooth devices have the pairing mechanism to make sure the privacy of patients is protected.. Wi-Fi connection is used to sending data to health care center after the raw data is processed. Since Wi-Fi service is now widely deployed among big cities, it can be accessed with a relative low cost without sacrificing mobility. Socket protocol is used in this thesis.. Fig. 2-2 Hardware Architecture. 2-3. Software Architecture In the previous section, we mentioned that we will use mobile phone as our signal processing. platform. Nokia N95 8G is chosen for its fully support of program development, including the most dominating computer language such as C, Java, Python…etc. We have developed an application running on Symbian OS, which is the operating system of Nokia mobile phone, to handle data receiving, sending and so do biomedical signal processing and diagnosis. Also, we have developed a server application running on PC to verify this system. This application is responsible for receiving processed data from the mobile phone, saving data into database, reproducing model and updating to the mobile phone’s database. In conclusion, the software contains. . z. A user friendly user interface.. z. A program working on signal processing. 15.

(80) . z. Eliminating noise.. z. Signal classification processing.. z. A program to communicate with server and sensor nodes.. z. Socket connecting.. z. Bluetooth connecting.. z. A database that records the daily biomedical signals of mobile phone holder.. The whole software architecture is as Fig. 2-3.

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(88) Fig. 2-3 Software Architecture. 2-3-1. User Interface. The main and only requirement for the user interface is user friendly. How friendly will it be? User doesn’t have to touch any button except for launching the program itself. The rest actions are handled by pre-programmed application behind the scene. It shows current condition of the certain biomedical signal such as ECG and CRP. And it notifies user by sound and displaying error. . 16.

(89) . message on the screen while there’s something wrong about the health condition or other technical difficulties, i.e. wireless/Bluetooth connection failure.. 2-3-2. Signal processing. There are two parts of signal processing: the pre-process for de-noise and the main classification program. The pre-process is made to eliminate the electric and other possible environmental noise with some criteria. And the main classification program consists of two major components: feature extraction and support vector machine classification. Feature extraction means we have to extract the seemly unspecific raw biomedical signal into some characterized series of numbers which are able to be identified as the certain diseases or abnormalities. Afterwards, support vector machine, the supervised machine learning algorithm, is then applied to the extracted features, creating a model which contains information about the extracted features. The flow chart of this signal processing is shown as Fig. 2-4. To give a deeper explanation, please check chapter 4-3 .. Fig. 2-4 Signal Processing Architecture. 2-3-3. Data communication. This mobile biomedical signal analysis system has two main functions – communicating with sensors and servers, and biomedical signals diagnosis. Therefore, the communication plays an important role in application development on mobile phone. It has been mentioned before; this device communicates with the Bluetooth receiver built inside smart phone, and communicates with server through Internet. Next, the development environment for these two kinds of communication on Symbian OS is introduced.. . 17.

(90) . Bluetooth Communication Bluetooth wireless technology is a short-range communications system intended to replace the cables connecting portable and/or fixed electronic devices. The key features of Bluetooth wireless technology are robustness, low power, and low cost. Many features of the core specification are optional, allowing product differentiation. The Bluetooth core system consists of an RF transceiver, baseband, and protocol stack. The system offers services that enable the connection of devices and the exchange of a variety of data classes between these devices.[6] Bluetooth architecture is mainly developed by the Bluetooth SIG (special interest group) which consists of Nokia Mobile Phones, IBM Corp., Intel corp., Toshiba Corp. and Ericsson Mobile Communications AB. It allows for developing interactive services and applications over interoperable radio modules and data communication protocols. We concern about the Bluetooth protocol stack only and it is briefly explained here. The object for this protocol stack is allowing different devices with different hardware architectures running over identical protocol stacks could communicate with each other. Different applications may run over different protocol stacks. However, each one of these different protocol stacks use a common Bluetooth data link and physical layer. As seen in Fig. 2-5. There are many protocols we can use to communicate. The upper the protocol is, the easier user and developer can use. In this thesis, we use the SPP (Serial Port Protocol). SPP is a protocol under RFCOMM protocol, thus does not exhibit in Fig. 2-5.. . 18.

(91) . Fig. 2-5 Bluetooth Protocol Stack[25] Serial Port Protocol for Bluetooth is to emulate a connection between devices while there th is no physical connection but wireless connection. The application of this protocol on both sides of devices is typically legacy applications, which is able and wanting to communicate commu over a serial cable (As I mentioned, it is emulated). emulated . But legacy applications do not know how to set up Bluetooth emulated serial connection. A smart phone with Bluetooth built in is aware of the setting-up setting procedure. However the transceiver which transmits the biomedical signals isn’t. isn Because of that, the smart phone will always be the initiative connector conne while the sensor does not. The figure below shows the model of how SPP works.. . 19.

(92) . Fig. 2-6 Serial Port Protocol Model[26] Device A (DevA): this is the device that takes initiative initiative to form a connection to another device Device B (DevB): this is the device device that waits for another device to take initiative to connect. Then setting up virtual serial ports on two devices and connecting these with Bluetooth, to emulate a serial cable between the two devices. Any legacy application may be run on either device, using sing the virtual serial port as if there were a real real serial cable connecting the two devices (with RS232 control signaling). Only one connection at a time is dealt with in this profile. Consequently, only point-to-point point configurations are considered. However, However, this should not be constructed as imposing any limitation concurrence; concurrence; multiple executions of this profile should be able abl to run concurrently in the same device. This also includes taking on the two different roles (as DevA and DevB) concurrently [26]. As for the security issue, the Bluetooth specification security feature supports authentication authenticat for both unidirectional and mutual, and encryption. These security features are based on a secret link key that is shared by a pair of devices. The key key is generated when a paring procedure occurs at the time the two devices communicate for the first time. In Fig. 2-7 explains the procedure: z. . Connect request to L2CAP.. 20.

(93) . z. L2CAP requests access from the security manager.. z. Security ecurity manager: lookup in service database.. z. Security ecurity manager: lookup in device database. d. z. Iff necessary, security manager enforces authentication authentication and encryption.. z. Security ecurity manager grants access.. z. L2CAP continues to set-up set the connection.. Fig. 2-7 (left) Security Architecture; Architecture (right) Information ation flow for access to trusted service[27] service Socket Programming Symbian OS implementing J2ME provides a rich variety of communication techniques for transferring data between mobile devices and desktop PCs or servers.. In this thesis, TCP/IP (Transmission Control Protocol/Internet Protocol) sockets sockets are selected. This is a common solution to communication between mobile application and another application running on a desktop de PC. The J2ME, which is a branch of Java language lang providing ing framework of development over mobile devices, provides general-purpose general purpose networking application programming interface interfac (API), called the generic connection framework (GCF), based on the socket interface from the University of o California at Berkeley. GCF is designed to run efficiently on Java approved operating systems while . 21.

(94) . maintaining compatibility with the Berkeley Software Distribution (BSD) standard, known as Berkeley Sockets. Every J2ME network communication passes through the GCF interface. A socket on a client device can connect to a socket on a server device, and one connected, reliable two-way transfer of data can be made. There might be only one physical connection to network, but there can be many socket connections to a server. And two important pieces of information must be provided for socket communication: z. IP Address: This address is provided either as the actual address (for example, “192.168.42.31”) or as the domain name (for example, “www.google.com”). For the latter, the accessible domain name server (DNS) should be ensured.. z. Port Number: Each service type on a server that uses sockets has a unique integer number assigned for each service. This is the port number. Standard protocols (such as HTTP) have a standard port number (such as 80). The port numbers above 1024 can be assigned for our own applications. Server Application. Client Application. Open a listening socket socket() Open a socket socket(). Name the socket bind(). Wait for next connection. Listen for incoming connection listen() Accept incoming connection accept(). Connect to listening socket connect(). Return socket send() & recv() data. socket. Close connection close(). socket. Close connection close(). Fig. 2-8 socket application flowchart for server and client[28] The socket function-calling sequence for server applications and client applications is given in Fig. 2-8[28]. The server application creates a listening socket and waits for a client to connect. The . 22.

(95) . client creates a socket and connects to the server listening socket. At this point, the server creates another socket to which the client socket connects, and the server’s listening socket goes back to wait for another client. When the connection is established, both the server and the client can send and receive data through the connection. And either the client or the server can terminate the connection.. 2-3-4. Records of Daily Biomedical Signal. Database is as important as it can be. In this thesis, database is designed to record daily biomedical signal of patient. We don’t drop any of the signals even if they are old with respect to current signals. That is, each time a data set comes in, at the time patient came home and plugged his smart phone, it is multiplied by a Forgetting Factor. The newest data set is multiplied by 1, which means it is the most important data set; the second latest one is multiplied by one forgetting factor while the third latest one is multiplied by forgetting factor twice. So why do we do this? Human biomedical signals are always changing. The causes of constantly changing may be physical. Physically, we can grow older, fatter. This does turn the actually normal biomedical signal into seemingly abnormal biomedical signal. The database is designed to eliminate this effect. Older data sets produce smaller influence while newer data sets own greater weight. The whole idea is illustrated as Fig. 2-9. . . . . 7&4 ) . ) . Fig. 2-9 Database diagram . . 23.

(96)

(97) . Chapter 3. Signal Analysis Theorem. In this chapter, we are going to introduce our signal analysis theorems. First, we will start with the spectral estimation theorem which is used to extract some useful features from EKG data in order to identify which data are from healthy people and which are from unhealthy people. Next, we will introduce the clustering algorithm which is used for classification. This thesis clusters the data sets based on the features we extract with the spectral estimation. And there are two clusters for our data sets, one is healthy, and another is unhealthy.. 3-1. Random Process Since spectral estimation is considered with respect to random process, some basic random. process theory should be introduced first. Here is a simple review of some random process concepts we will use in the later sections. For a deterministic signal[29], there is only one value at one point of time from the function of. the signal, for instance, the value of

(98) at t = 0.5 is 0.6065 . However, for a random. process, the value at an arbitrary time is not a constant. There are many possibilities for the. value. These possible values at are determined by the probabilities and events which occur at. time . As Fig. 3-1 shows, if event s1 happens at time , the value is approximately 0.5. If event. s2 happens at that time, the value is approximately -0.3. If event happens, the value at that time is approximately -0.005. That is, a random process is described by a sampling space S which is a. union composed of several events. If there are n events in a set S , each event will then correspond. to a sampling function for ,

(99) . It follows from what has been said. that the value is random at an arbitrary time and cannot be observed until the event occurs,. therefore at time a set of values constitutes a set of random. . 25.

(100) . variables. Note that a random variable corresponds to a value; while a random process corresponds to a waveform with respect to time. Assuming that the n events in set S occurred with the. probability which is quantified by the joint probability distribution function , the. joint probability density function is the derivative given by

(101) ! . Now,. considering at time , the random variable is , the expectation (or mean value) is given by. "

(102) # $ %. . (3-1). Sampling Space S. x(t)=exp(-t) Deterministic signal. x(t,s1) 1st experiment result Composed of n sampling points {s1, s2,…, sn}. x(t,s2) 2nd experiment result. x(t,sn) nth experiment result tk. t. {x(tk,s1), x(tk,s2), … , x(tk,sn)} form a random variable. Fig. 3-1 Random Process. As Fig. 3-2 shows, & and & are two arbitrary points on time axis. We shift the waveform. right by & and & respectively, and multiply by the original waveform , and then take. expectation. We can get two different autocorrelation function values '(( & and '(( & ,. . 26.

(103) . therefore we can also know that there would be different autocorrelation function values with respect to different time shifts.. ! ! rxx([[! ]=E{x(t,s1)x(t --! ! 1,2 )=E{x(t,s1)x(t ! 1,2,s1)} x(t,s1) x(t-!1). x(t-!2). !! 1 1. !2 2. ! ! rxx([[! ]=E{x(t,s2)x(t --! ! 1,2 )=E{x(t,s2)x(t ! 1,2,s2)} x(t,s2). x(t-!1). x(t-!2). ! ! rxx([[! ]=E{x(t,sn)x(t --! ! 1,2 )=E{x(t,sn)x(t ! 1,2,sn)} x(t,sn ). x(t-!1). t. x(t-!2). t. Fig. 3-2 Random Process Any signal is generally the function with respect to time; therefore it can be regarded as a realization of a random process. However, a random process is composed of n sampling functions, that is to say the probability distribution is hard to be inferred. Therefore, neither the expectation value nor the autocorrelation function value can be easily obtained by standard probability density function. However, as long as a random process is ergodic, which is to be discussed in next paragraph, we can calculate the expectation value or the autocorrelation function value with simple additions and multiplications using one single data. The mean value calculated using this method is called time average; otherwise it is called ensemble average. . 27.

(104) . Ergodicity A random process is said to be ergodic if, with probability 1, all its statistics can be predicted from a single waveform of the process ensemble via time averaging; that is, the time averages of almost all possible single waveforms are equal to the same constant (the ensemble average). The mathematical analysis of random process is greatly simplified with the property of ergodicity. And the concept of ergodicity requires the assumption that the data be stationary. So, if measured process is stationary, time averages of mean and autocorrelation can replace their ensemble averages. )*+,-. /0 1/ 5/ 23

(105) " 23

(106) 4 )*+,-.. . /0. 8 8 1/ 5/ 2 6 73 23

(107) " 2 6 73 23

(108) '(( 273. (3-2) (3-3). Discrete-time Random Process A discrete random process may be thought of as a collection of real or complex discrete sequences of time, any one of which might be observed on any trial of an experiment. The mean or expected value of a discrete random process 23 at time index is defined as. 4 23

(109) " 23. (3-4). Autocorrelation. as. as. . The autocorrelation of a random process at two different time indices and is defined '(( 2 3

(110) " 2 3 8 2 3. (3-5). 9(( 2 3

(111) " 2 3 : 4 2 3 8 2 3 : 4 8 2 3

(112) '(( 2 3 : 4 2 3 4 8 2 3. (3-6). The autocorrelation of the process 23 with the mean removed is the autocovariance, defined. 28.

(113) . Cross Correlation When two different random processes 23 and ;23 are involved, one may define the cross. correlation as. '(< 2 3

(114) " 2 3; 8 2 3. (3-7). And one may define the cross covariance as =>? 2 3

(115) " 2 3 : 4 2 3@2 3 : ;A 8 2 3

(116) '(< 2 3 : 4 2 3;A 8 2 3. (3-8). Wide sense stationary The definitions to this point have shown an explicit dependence on the time indices. A random process is wide-sense stationary (WSS) if its mean (expectation value) is constant for all time indices (i.e. independent of time) and its autocorrelation depends only on the time index difference 7

(117) : . A pair of random processes are jointly wide-sense stationary if the cross correlation. depends only on the time index difference. Processes that are jointly stationary must also be individually stationary. In summary, WSS discrete random process 23 is statistically characterized by a constant. mean. 4 23

(118) 4. (3-9). Meaning BA is constant for all time indices. And an autocorrelation sequence (ACS) depends only on time index difference '(( 273

(119) " 2 6 73 8 23. (3-10). 9(( 273

(120) " 2 6 73 : 4 8 23 : 4 8

(121) '(( 273 : C 4 C. (3-11). And an autocovariance sequence. The jointly WSS discrete random processes 23 and ;23 are statistically characterized by. a cross correlation sequence (CCS) . 29.

(122) . '(< 273

(123) " 2 6 73; 8 23. (3-12). And a cross covariance sequence that is a function of the time-difference index B@ 8 9(< 273

(124) " 2 6 73 : 4 ; 8 23 : ;A 8

(125) '(< 273 : AAA. (3-13). Some useful properties of autocorrelation are listed below. G E. '(( 23 H C'(( 273C 8 273 '(( 2:73

(126) '((. F'(( 23'<< 23 H I'(< 273I E ' 2:73

(127) ' 8 273 (< <( D. J. (3-14). These properties apply for all integers 7. It is easy to see from these properties that the ACS. of a WSS random process must be a maximum at the origin (7

(128) ). And the autocorrelation matrix is defined as K((

(129) " 23 L 23. 23. 2 : 3

(130) " MN Q 2 8 23 O. 2 : P 6 3. '(( 23 ' 2:3

(131) N (( O '(( 2:P 6 3. '(( 23 8 '(( 23

(132) N O 8 '(( 2P : 3. 8 2 : 3. '(( 23 '(( 23 O '(( 2:P 6 3. '(( 23 '(( 23 O 8 '(( 2P : 3. R R T R. 8 2 : P 6 3#3S. '(( 2P : 3 '(( 2P : 3 Q O '(( 23. R '(( 2P : 3 R '(( 2P : 3 Q T O R '(( 23. The cross correlation matrix is defined as. . R. 30. (3-15).

(133) . K(<

(134) " 23@ L 23. 23. 2 : 3

(135) " MN Q 2; 8 23 O. 2 : P 6 3 '(< 23 W ' 2:3

(136) V (< O V U'(< 2:P 6 3. '(< 23 W ' 8 23

(137) V <( O V 8 2P : 3 ' U <(. ; 8 2 : 3. '(< 23 '(< 23 O '(< 2:P 6 3. '(< 23 '(< 23 O 8 '<( 2P : 3. White noise random process. R R T R. R R T R. R. ; 8 2 : P 6 3#3S. '(< 2P : 3 Z '(< 2P : 3Y O Y '(< 23 X. (3-16). '(< 2P : 3 Z '(< 2P : 3Y O Y '(< 23 X. There is a special random process we are interested in. It is a zero-mean random process [23. of a discrete-time white noise. A white noise process is uncorrelated with itself for all lags, except at 7

(138) , for which its variance is \] . The ACS has the form ']] 273

(139) \] ^273. (3-17). where ^273 is the discrete delta sequence. The PSD of the white noise autocorrelation. sequence is, therefore, a constant for all frequencies. _]]

(140) \]. (3-18). The PSD function is discussed in more detail later.. 3-2. Spectral Analysis The general problem of spectral estimation is to determine the spectral content of a random. process, which is based on a finite set of observations. Through the spectral estimation result, a preliminary data analysis can be given to the observed random process. And spectral estimation. . 31.

(141) . plays an important role in many fields, such as biomedicine, vibration analysis, image processing, radio astronomy, oceanography, and ecological systems.[30][31] Next, we are going to introduce two kinds of spectral estimations. One is classical spectral estimation; while another is a more modern approach to spectral estimation — parametric spectral estimation.. 3-2-1. Classical Spectral Estimation. Generally, power spectral density (PSD), which will be denoted as _(( , is used to represent. spectral estimation. The frequency may either be thought of as the fraction of the sampling frequency used in obtaining the data samples from a continuous random process or as the number of cycles/sample. The PSD function describes the distribution of power with frequency of the random process. There are two popular classical spectral estimation methods based on Fourier analysis. They are the direct method (also called the periodogram method) and the indirect method (also called the correlogram method). The direct method operates directly on the data set to yield a PSD estimate. On the other hand, the indirect method must first make an estimate of the correlation sequence, and then Fourier transform it to obtain the PSD estimate. Direct Method The formal definition of the PSD, based on ergodicity, has the discrete form cd I e _((

(142) `a7/-. " b/0 I1/ 5/ 23 . . (3-19). Ignoring the expectation operation and assuming a finite data set B23 B2f : 3 of f. samples, the sample spectrum, i.e. Equation (3-20), may be computed from the finite data sequence. _g((

(143). . h. cd I1h I 5 23. . (3-20). . 32.

(144) . Indirect Method There is an alternative definition of PSD, which is defined as the discrete-time Fourier transform of the autocorrelation sequence: cdi _((

(145) 1. i5. '(( 273. (3-21). The correlogram method of PSD estimation simply substitutes a finite sequence of autocorrelation estimates (the correlogram) for the infinite sequence of unknown true. autocorrelation values. For example, substitution of the unbiased autocorrelation estimates 'j(( 273 that have been computed to maximum lag indices kl yields one possible PSD estimator _m((

(146) 1ni5n 'j(( 273 cdi. (3-22). 2 6 73 8 23 'j(( 273

(147) hi 1hi 5 . (3-23). Another PSD estimator may also be formed by using the biased autocorrelation estimate. 'o(( 273, yielding. _p((

(148) 1ni5n 'o(( 273 q : r7 'o(( #273

(149) s . . h. 1hi. 2 6 73 8 23 5. 1hCiC 8 2 h 5. 6 C7C3 23. (3-24) 7 t:. :t : 7 . J#. (3-25). Parametric Spectral Estimation In Section 3-1 , it was shown that the statistics of a random process could be represented alternatively by either the autocorrelation function (ACF) or the power spectral density (PSD), both of which are nonparametric descriptions. In this section, an alternative approach is introduced to describe the random process by means of a parametric model. A special class of models, driven by white noise processes, is described in this section. This class includes the autoregressive (AR) process model, the moving average (MA) process model, and the autoregressive-moving average (ARMA) process model. The output processes of this class of models have power spectral densities. . 33.

(150) . that are totally described in terms of the model parameters and the variance of the white noise process. Based on these models, spectral estimation becomes a three-step procedure. The first step is to select a model. The second step is to estimate the parameters of the assumed model using the available data samples. The third step is to obtain the spectral estimate by substituting the estimated model parameters into the theoretical PSD implied by the model. One major motivation for the current interest in this parametric approach to spectral estimation is the apparent higher resolution achievable with these modern methods than that achievable with the classical approach. Many discrete-time random processes encountered in practice are well approximated by a time. series model. In this model, an input driving sequence u23 and the output sequence 23 that is to model the data are related by the linear difference equation,. 23

(151) : 15 v2w3 2 : w3 6 15 x2w3u2 : w3

(152) 1. 5 y2w3u2 : w3 {. z. (3-26). This is the most general linear model, called ARMA model, and is shown in Fig. 3-3. u23 is. not the observation noise, but an innate part of the model and gives rise to the random nature of the observed process 23. 23 is the output sequence that models the observed data.. The system function |} between the input u23 and the output 23 for the ARMA. process is the rational function |}

(153) . ~. (3-27). for which the polynomials are. . 34.

(154) {. }

(155) 6 v2w3} 5 z. }

(156) 6 x2w3} 5 .. |}

(157) 6 y2w3} 5. It is assumed that } and } have all their zeros within the unit circle of the z-plane to. guarantee that |} is a stable and causal filter.. Fig. 3-3 ARMA model. The z-transform of the output sequence 23 autocorrelation is related to the z-transform of. the input random process u23 autocorrelation by _(( }

(158) _ }|}|8 8

(159) _ } . 8 8 . ~~8 8. (3-28). The input driving sequence here is a white noise process of zero mean and variance , so that. _ }

(160) \ . By substituting }

(161) cd into Equation (3-28), the ARMA power spectral density is obtained.. . 35.

(162) ~d . _((

(163) . d. \

(164). \ d d d d. (3-29). The polynomials and are defined as

(165) 6 15 v2w3 cd

(166) {L v {.

(167) 6 15 x2w3 cd

(168) zL x . (3-30) (3-31). And the complex sinusoid vectors {L and { and parameter vectors v and x are. defined as. {

(169) 2 cd R cd{ 3 z

(170) 2 cd R cdz 3 J J v

(171) 2 v 23 6 v 23 R v 23 6 v 233 x

(172) 2 x 23 6 x 23 R x 23 6 x 233. (3-32). The ARMA model is sometimes referred to as a pole-zero model. If all the v2w3 coefficients except v23

(173) vanish for the ARMA parameters, then. 23

(174) 15 x2w3u2 : w3 z. (3-33). And the process becomes an MA process of order q, and the power spectral density of MA model becomes _((

(175) CC \. (3-34). This model is sometimes termed as an all-zero model and is shown in Fig. 3-4.. Fig. 3-4 MA model. If all the x2w3 coefficients except x23

(176) are zero in the ARMA model, then . 36.

(177) . 23

(178) : 15 v2w3 2 : w3 6 u23 {. (3-35). And the process becomes an AR process of order p. With this model, the present value of the process is expressed as a weighted sum of past values plus a noise term. The PSD of AR model is then _((

(179) CdC . . (3-36). This model is sometimes termed as an all-pole model and is shown in Fig. 3-5.. Fig. 3-5 AR model Relationship between model parameters and autocorrelation sequences Next, we are going to discuss how to obtain the model parameters when the autocorrelation sequence is known. Consider ARMA model {. z. 23

(180) : v2w3 2 : w3 6 x2w3u2 : w3 5. .

(181) 1. y2w3u2 : w3. (3-37). Multiply Equation (3-37) by 8 2 : 73 and then take the expectation, then the result is " 23 8 2 : 73

(182) : 15 v2w3" 2 : w3 8 2 : 73 6 15 x2w3"u2 : w3 8 2 : 73 {. z. Or. . 37. (3-38).

(183) . '(( 273

(184) : 15 v2w3'(( 27 : w3 6 15 x2w3'( 27 : w3 {. z. (3-39). The cross correlation '( 2a3 between the input and the output can be expressed in terms of the. y2w3 parameters. '( 2a3

(185) "u2 6 a3. 8 23.

(186) " u2 6 a3 u. 8

(187) ' 2a3 6 1. 5 y 2w3' 2a 6 w3. 8 23. .. 6 y8 2w3u8 2 : w3 5. As u2w3 was assumed to be white noise sequence, then. (3-40). a a

(188) J '( 2a3

(189) s \ 8 2:a3 \ y a . (3-41). 8 '(( 2:73 7 { z 8 '(( 273