Question Wavelet and G

Q A wave is defined as a periodic oscillating function of time or space whereas wavelets are localized waves having their energy concentrated in time or space and highly suited to the analysis of non-stationary transient signals. The theory behind wavelets is to analyse the real-time signals according to scale. With wavelet analysis, we can use approximation functions that are contained neatly in finite domains. Wavelets are well-suited for approximating data with sharp discontinuities.

As a result, working with wavelets produces functions and operators that are small in magnitude or amplitude and that makes wavelets very well suited for typical applications such as data compression and denoising / noise reduction in signal processing. The ability to vary the scale of the function as it addresses different frequencies also makes wavelets better suited to signals with spikes or discontinuities than traditional transformations such as the Fourier Transform. Wavelet transform gives good frequency resolution and poor time resolutions at low frequencies and at high frequencies, it gives good time resolution and poor frequency at high frequency.

In most of the signal processing applications the frequency details are much important even though the Fourier transform serves with frequency spectrum, applications such as electrocardiograph, PDG data refining / processing, the raw signals needed to be analysed with time resolution as well. As Fourier Transform is unable to give good results to the non-stationary signals, the wavelet transform is being used in varied applications. The method or technique which will be used for the PDG processing/analysis as well as the ECG/Foetal ECG signal processing and analysis implicates wavelet transforms (WT) with the help of MATLAB frequency modulation technique which helps in acquiring DD( drawdowns) and BUs (build-ups). The workflow regarding processing generally involves data visualisation and acquisition, outlier removal (including both step and spike outliers), denoising process, smoothing, data reduction and uncertainties regarding breakpoint detection (due to drop in flowrate and well shut in procedures). Wavelet transform methodology with the help of MATLAB platform is responsible for performing various steps mentioned above. On the other hand flow history reconstruction, filtering and data interpretation are performed by non-linear regression analysis. The next step involves the extraction of pressure transient data (DD & BU) which can be analysed later with the help of traditional methods and requisite software followed by history matching. In the end, the results pertaining to skin factor and effective permeability of the reservoir can be evaluated in time lapse fashion to reveal the information revealed due to the dynamic behaviour of the reservoir properties.

In the past couple of decades, an enormous interest has emerged in the application of wavelets due to its successful implementation into various fields of data analysis ventures ranging from data compression and signal processing through to the more mathematically pure field of solving partial differential equations. Wavelets provide an alternative approach to traditional signal processing techniques such as Fourier analysis for breaking a signal up into its constituent parts. The driving theory behind wavelet analysis is their property of being localised in time (space) as well as scale (frequency). This provides a time-scale map of a signal, enabling the extraction of features that vary in time. This makes wavelets an ideal tool for analysing signals of a transient / non-stationary nature. WT has the ability to perform local analysis and has got a windowing technique which allows the use of long time intervals where there is a need for low frequency data acquisition to be precise and correct. It can also manage shorter regions where high frequency information is needed. Wavelet analysis is capable of revealing hidden aspects of data which is generally missed by the other signal processing techniques i.e. aspects like breakdown points, discontinuities in higher derivatives, self-similarities, trends etc.

Foetal ECG

The foetal heart rate (fHR) and the morphological analysis of the foetal electrocardiogram (fECG) are two of the most important tools used nowadays in clinical investigations to examine the health state of the foetus during pregnancy. The fHR is the mostly used parameter in foetal monitoring. This method to obtain the instantaneous fHR and the fECG morphology is the abdominal recording of the fECG which considers an array of electrodes placed on the maternal abdomen. This recording procedure overcomes the main drawbacks of the methods used in clinical routine for foetal monitoring. However, the limitation of this technique is the very low signal-to-noise-ratio (SNR) of the available recorded fECG. This is mainly due to the fact that the fECG signal is generated by a small source (foetus heart). In addition, it has to propagate through different attenuating media to reach the maternal belly surface. Hence, the fECG signals contained in abdominal signals (ADSs) provide an amplitude of about 10 μV which diminishes further as the weeks goes by a

Diagnosis of mother's and child's heart beat is very necessary during pregnancy and hence we use Foetal electrocardiogram (FECG) extraction for the same. The signal contains precise information that can help doctors during pregnancy and labor. In this thesis, an easy-to use method has been implemented using adaptive noise canceller (ANC). Using the ANC, an effective algorithm has been proposed. The algorithm uses ANC, Least Mean Square (LMS) method and a Simulink model for the extraction of FECG. The FECG extraction method has been implemented using an algorithm implemented on MATLAB using Simulink models. The extracted FECG signal is a noise free signal. The QRS complex has been detected using another algorithm that counts the R-R peaks. The simulation result shows that heart rate of the FECG signal can be counted using the detection algorithm.

This project evokes a complete model of the FECG extraction with the implementation of effective algorithms and adaptive filters and finally gives the heart rate of the FECG signal.

Foetal ECG monitoring is a widely used technique for diagnosis and to find out foetal abnormalities. The physician can easily prepare himself/herself for the possible abnormalities in a foetus by taking diagnosis of the foetal ECG signal during the pregnancy stage. It's the simplest non-invasive method to diagnose various heart diseases. The various electrical activity of the heart is represented by the Foetal ECG (FECG) and hence it provides valuable information about its physiological state. The FECG signal can be easily obtained from the abdomen of a pregnant women and the chest gives the maternal electrocardiogram (MECG) signal. The addition of the MECG signal with the FECG signal is typically annoying one. By placing electrodes on the maternal abdomen, the FECG signal, thus generated, gives minute details about the foetal condition which are very useful during diagnosis. The abdominal ECG signal contains various unwanted interferences, maternal ECG (MECG) signal and electromyogram (EMG) and the FECG signal is corrupted by various noise and the skin impedance.

There are various methods to extract FECG like wavelet transform, Doppler ultrasound, adaptive filtering, correlation methods, blind source separation technique and a combination of blind source separation methods and wavelet analysis. The heart rate of the FECG can be determined by calculating the R-R peaks of the QRS complex [4]. But, as the FECG signal is merged with MECG signal and various interferences, it is very difficult to calculate the heart rate from the raw signal. Hence, the FECG is extracted from the raw signal to get the proper heart rate of the foetal signal.

Seeing a typical foetal ECG (FECG) signal, the doctor rectifies the foetal heart abnormalities. The ECG device extract the FECG signal from the Abdominal ECG (AECG) signal and shows them on the monitor. The heart rate of the foetal heart comes to be greater than the maternal heart rate. The challenges like the extraction of a low amplitude and high frequency signal from the high amplitude and low frequency signal signifies the basis of this technique.

1.5 OBJECTIVE Two ECG signals were taken; one from the chest of the mother and another from the abdomen of the mother that contains both the foetus heartbeat signal and maternal heartbeat. The objective of our study is to separate both these parts and thus extract the foetus heartbeat signal and then detect the R-peaks in order to determine the foetus heart rate.

To extract the foetus heartbeat signal from the ECG signal taken from the abdomen. 6

· Regenerating the waveforms of both ECG signals in MATLAB using the data taken from the ECG machine. Separating both signals and reducing any noise present in the signal to obtain the foetus heartbeat signal using ANC.

To count the R-peaks and calculating the heart rate of the foetus by using the R-R separation. Applying a differentiation technique to the QRS-complex to differentiate the extracted signal up to 3rd order to get the peaks.

Setting a threshold and comparing the peaks with it to detect the R-peaks. Finally counting the R-peaks per one minute to obtain the heart rate of the baby.

PLI Reduction by Applying the Wavelet Transform Interference of power line (PLI) (fundamental frequency and its harmonics) is usually present in bio potential measurements. Despite all countermeasures, the PLI still corrupts physiological signals, for example, electromyograms (EMG), electroencephalograms (EEG), and electrocardiograms (ECG). When analysing the foetal ECG (fECG) recorded on the maternal abdomen, the PLI represents a particular strong noise component, being sometimes 10 times greater than the fECG signal, and thus impairing the extraction of any useful information regarding the foetal health stat

In the recent years, discrete wavelet transforms and thresholding techniques have been used for ECG denoising b

Wavelet based noise cancelling techniques became very popular because they are able to decompose the signal into time-frequency domain which is appropriate for the analysis of non-stationary signals. It is reported in the literature that discrete wavelet transform does not introduce any artificial information to the original signals; the threshold is generated based on the attributes extracted from the signal.

The main problem is the identification of the mother wavelet, the level of decomposition, and the optimal threshold. Garg et al. c compare different mother wavelet functions for ECG denoising and conclude that the recovery of the ECG with minimal artefacts is obtained when using Sym10 decomposition at level 5. The extraction of foetal ECG signal from maternal ECG signal which is actually a mixture of both mother and foetus heartbeat signals is generally done with the help of ANC. ANC (Adaptive Noise Canceller)

This method is used for non-stationary type noise or interference which is not necessarily a random process. Adaptive filters are systems with a linear filter that uses a transfer function which is controlled by different variable parameters and these parameters can be adjusted according to an optimization algorithm [12]. Most adaptive filters are digital filters owing to the complexity of the optimization algorithms used. In case of an ANC no info about the signal and noise characteristic is available and both the noise and signal are uncorrelated. Another reference signal is obtained from a second source which is strongly correlated with the noise but uncorrelated with the signal. When the signal and noise are stationary, an adaptive filter acts as a fixed filter whereas it acts as a notch filter or comb filter for a periodic interference. Least Mean Squares (LMS) and Recursive Least Squares (RLS) filters are a few examples of adaptive filters and all these filters described above can only be applicable for additive noise.

METHODOLOGY

The electrocardiogram (ECG) signal for both the mother and foetus are retrieved from the given data that is sampled at 5000 Hz using a smoothing filter to give the discrete data a somewhat smoother shape. The filter used here is a digital filter known as the Savitzky-Golay Filter. The main purpose of using this filter is to smooth the signal by increasing the signal-to-noise ratio (SNR) without distorting the signal significantly. This filter uses a convolution method to achieve the goal. The heart rate of a foetus is significantly higher than that of the maternal heart rate which is in this case approximately a rate of 85 beats per minute whereas for the foetus it is approximately 132 beats per minute. In general, the foetus heart beats faster than that of the mother, with a range of rates from 120 to 160 beats per minute. The foetal electrocardiogram signal has a much weaker amplitude as compared to its maternal counterpart. For example here the mother ECG signal has a peak of 3.5 millivolts whereas the foetal ECG signal has a peak of just 0.25 millivolts. ECG signals are taken from two different locations of the mother's body, the chest and the abdomen. The chest signal gives the original mother ECG signal whereas the signal obtained from the abdomen is a mixture of both mother and foetus heartbeat signals usually dominated by the maternal component propagated from the chest cavity to the abdomen. A linear FIR filter can be used with 10 randomized coefficients in order to describe this path. There may be some additional broadband interference associated with both mother and foetus signals that can be eliminated by the addition of a small amount of uncorrelated Gaussian noise. The task performed by the adaptive filter is to adaptively remove maternal component from the foetus heartbeat signal. To do so it needs a reference signal which is nothing but the signal generated from the maternal ECG itself. Like the foetal ECG signal the maternal ECG signal is also expected to contain some additive broadband noise .

ALGORITHM USED FOR EXTRACTION The extraction method described in this thesis is based on a MATLAB code that consists of 4 simple steps as described in the flowchart of the proposed algorithm shown below in Fig.

Generation of the ECG signals using MATLAB MATLAB is an easy-to use tool which is very helpful in the extraction of the Foetal ECG (FECG) signal from the Abdominal ECG (AECG). Using MATLAB we generate the signal on which the task can be performed and implemented easily. MATLAB contains a function Savitzky-Galoy filter function and using this command the required signals are generated.

Foetal Electrocardiogram Signal Heart rate is calculation of the beating of the heart. Heart beats in a fixed time duration and the calculation of number of beats i.e. number of R peaks per minute gives the heart rate of the ECG signal.

Finally the signal is cleaned up and a threshold level is set so that any value above it can be considered as a peak and hence the number of peaks in the signal can be counted. The heart rate counting has been performed using the QRS detection techniques that has been discussed in Chapter 3. The most optimized technique has been to count the R peaks of the FECG signal. Counting the R peaks the heartbeat of the Foetus is calculated. The heart beat comes to be 135 beats per minute. This is comes in the range exactly [32]. As the foetal heart rate is greater than the maternal heart rate and it comes in the range 120-160 beats per minute, this experiment verifies the same aptly. Finally, all the plots are shown below that explains the signal forms of the foetal ECG (FECG) signal.

Heartbeat calculation is never a difficult task if the foetal signal has been extracted from the abdominal ECG (AECG) signal. Because, the first step is always to extract the FECG signal and then applying optimized QRS complex detection techniques heartbeat can be calculated.