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Fetal Phonocardiography is a simple and non-invasive diagnostic technique for surveillance of fetal well-being. The fetal phonocardiographic (fPCG) signals carry valuable information about the anatomical and physiological state of the fetal heart. This paper is concerned with a study of continuous wavelet transform (CWT) based scalogram in analyzing the fPCG signals. The scalogram has both spatial and frequency resolution power, whereas traditional spectral estimation methods only have frequency resolution ability. The fPCG signals are acquired by a Data Recording Module (DRM). Segmentation of these signals into fundamental components of fetal heart sound (S1 & S2) is carried out through envelope detection and thresholding techniques. CWT based scalogram is used for time-frequency characterization of the segmented fPCG signals. It has been shown that the wavelet scalogram provides enough features of the fPCG signals that will help to obtain qualitative and quantitative measurements of the time-frequency characteristics of the fPCG signals and consequently assist in diagnosis. The proposed method for time-frequency analysis (TFA) and the associated pre-processing have been shown to be suitable for the characterization of fPCG signals, yielding relatively good and robust results in the experimental evaluation.
Keywords: Time-frequency analysis, wavelet scalogram, fetal phonocardiography, heart sound, segmentation.
Fetal Phonocardiography (fPCG) is a suitable tool to analyze fetal well-being and has been proposed as an alternative technique to the widely accepted fetal cardiotocography1. The main advantages of fPCG technique are its non-invasiveness and simplicity2. This technique can be used for long-term home monitoring of the fetus3. The fetal Phonocardiogram i.e. fPCG signal is a linear summation of vibrations produced by fetal heart, maternal organs and external sources. These signals exhibit marked changes with time and frequency, hence classified as non-stationary and non-deterministic signals4.
Time-frequency analysis (TFA) is the most popular method for analyzing non-stationary signals5. It is also a useful and powerful tool for accessing health status of the unborn. One major benefit of applying a time-frequency transform to a signal is discovering the pattern of frequency changes, which often clarifies the nature of the signal6. There are number of methods available for TFA, each one has its own advantage and drawbacks.
The most popular and simplest method for TFA is the Short Time Fourier Transform (STFT)7. This method performs a mapping of one-dimensional signal to a two-dimensional function of time and frequency and therefore is able to provide true time-frequency representations for the signal. The main drawback of STFT is that it provides constant resolution for all frequencies since it uses the same window for analysis of the entire signal. The bilinear Wigner-Ville Distribution (WVD) can provide optimal concentration and less phase dependence than STFT, but it suffers from the cross-terms which may lead to false identification of the signal components in TFA8. The essential requirement of a good TFA is to obtain a sufficient concentration of the signal components, without significant cross-terms, so that the signal can be interpreted properly9.
The wavelet transform (WT) has been found particularly useful for the analysis of non-stationary signals because of its ability to localize in both time and frequency10. Wavelets are the functions of time and scale; it produces a time-scale representation of signals. The time-scale representation of signals can be considered as time-frequency representation, because wavelets with different scales measure the corresponding frequency components in the signal. The key feature of WT is that it uses short windows at high frequencies and long windows at low frequencies11. Scalograms are the plots that can show the magnitude of wavelets at various scales as a function of time. They are used with continuous wavelet transform analysis and are similar to spectrograms in TFA. Instead of plotting frequency versus time, they plot scale versus time12.
In this paper, the fPCG signals are acquired from the maternal abdominal surface using an inexpensive and simple to use DRM specially developed for this purpose. These signals are pre-processed for automatic gain control, de-noising and envelope detection. The detected signals are then segmented into the fundamental components of the fetal heart sound (S1 & S2). The TFA of these components of fPCG signals is carried out using wavelet scalogram. Here, a three-dimensional plot of the scalogram is used, together with the classical time and frequency domain representations. It can be seen that the scalogram can better exhibit the non-stationary fPCG signal whose frequency components changes with the time.
The rest of the paper is organized as follows: In the next section a brief review of the continuous wavelet transform and wavelet scalogram is provided. Section 3 illustrates the methodology for time-frequency characterization of fPCG signals based on wavelet transform. The obtained results are discussed in section 4. Finally conclusions are drawn in section 5 followed by a list of references.
2. Theoretical Background:
2.1 Continuous Wavelet Transform: The continuous wavelet transform (CWT) correlates the signal with families of waveforms that are well concentrated in time and frequency. These families of waveforms are obtained by the dilations and translations of an analyzing wavelet, Ïˆ(t). The CWT of a continuous signal is defined as
Where: - a continuous wavelet transform, 'x(t)' - a signal under study, 'a' - a scale coefficient connected with stretching or compression of signal in time, 'b' - a shift connected with time location, - a wavelet function or mother wavelet representing a wavelet family, '*' - denotes the complex conjugation and the factor is used for energy normalization. The wavelet function must satisfy following mathematical criteria:
A wavelet function must have finite energy
A wavelet function must have a zero mean, i.e., has no zero frequency components.
The process of CWT involves the following steps:
Shifts a specified wavelet continuously along the time axis.
Computes the inner product of each shifted wavelet and the analyzed signal.
Dilates the wavelet based on the specified scale.
Repeats steps 1 through 3 till the process reaches the maximum specified scale.
The output of the CWT is the CWT coefficients, which reflect the similarity between the analyzed signal and the wavelets. Unlike the discrete wavelet transform, the CWT can perform at every scale up to some maximum scale with minimum increment, which can be determined by trading off the need for detailed analysis with available computational horsepower. The CWT is also continuous in terms of shifting: during computation, the analyzing wavelet is shifted smoothly over the full domain of the analyzed signal13.
2.2 Wavelet Scalogram: The time-frequency energy density representation obtained by the WT is called scalogram and it is given by the square of amplitude of the WT. Scalogram is analogous to the spectrogram in time-frequency analysis using STFT. In signal processing, scalograms are useful in pattern-matching applications and discontinuity detections. If a signal contains different scale characteristics over time, the scalogram can present a time-scale view of that signal, which is more useful than the time-frequency view of that signal. The scalogram is given by:
The scalogram provides the energy evolution with time in a single process by viewing a map of the square of the wavelet coefficients. This facilitates identification of time-varying energy flux, spectral evolution, and transient bursts not readily discernible using time or frequency domain methods14.
The fPCG signal is a multi-component signal comprising of fetal heart sound, maternal organ sound and environmental sound. Moreover, because of the acoustic damping of the amniotic fluid and maternal tissues, the acoustic energy of the fPCG signal is very low15.
3.1 Data Acquisition: The fetal heart sound is in the form of mechanical vibrations passing through tissue structures. These vibrations are relatively weak because of the physical distance and small size of the fetal heart valve16. In order to sense this weak heart sound from maternal abdomen, the transducer should be properly placed and its mechanical as well as electrical impedance should be matched with that of the system. To facilitate this, a highly sensitive and efficient Data Recording Module (DRM) is developed17. The block diagram of the data recording module is shown in Figure 1.
Fig. 1. Block diagram of the Data Recording Module
The weak fPCG signals acquired from the microphone are pre-amplified, low-pass filtered and power amplified. These signals are de-noised with Discrete Wavelet Transform (DWT) based de-noising techniques. The de-noised signals are then saved in a personal computer in wave format for subsequent processing.
3.2 Signal Segmentation: The fetal heart sound, like adult heart sound consists of four main parts: the first heart sound (Sl), the systolic period, the second heart sound (S2), and the diastolic period in this sequence in time18. A Simulink model as shown in Figure 2 is developed for the segmentation of fPCG signals. For this purpose, Simulink Toolbox of MatlabTM version 7.8.0 (R2009a) is used. The model is built by interconnecting requisite blocks, which are available in the Simulink library and their parameters are fed while designing them for simulation. The input of this model is the de-noised fPCG signal, in the form of *.wav format; whereas outputs are the segmented S1s and S2s of the fPCG signal along with waveforms at various processing steps.
Fig. 2. Simulink Model for Segmentation of fPCG Signals
De-noised fetal heart sound signal, detected from mother's abdomen is fetched from corresponding wave file and applied to AGC subsystem. The function of this subsystem is to maintain the gain of the input signal to a pre-defined value. This will help in maintaining the constant threshold level of the segmentation algorithm. The gain controlled fPCG signals are then fed to envelope detection subsystem. This subsystem is based on envelope detection using Hilbert Transform. Computer simulation for the envelope generation subsystem is shown in Figure 3.
Fig. 3. Envelope Generation Subsystem
Output of envelope generator is connected to the threshold block. The Relay block allows its output to switch between two specified values. When the relay is on, it remains on until the input drops below the value of the Switch off point parameter. When the relay is off, it remains off until the input exceeds the value of the Switch on point parameter. This block converts the envelope signal into a series of discrete pulses.
These pulses are then fed to systolic and diastolic period separation subsystems, which are a combination of counters, relay and signal inversion blocks. Outputs of these subsystems are multiplied with the fPCG signal using signal multiplication blocks. This process results into signal segmentation in main components of fetal heart sound (S1 & S2). The waveforms at different steps are depicted in Figure 4.
Fig. 4. Waveforms at various processing steps
3.3 Time-Frequency Characterization: TFA is the most popular method for analyzing non-stationary signals. It transfers a one-dimensional time domain signal x(t) into a two-dimensional function of time and frequency19. Hence it can characterize signals over time-frequency domain.
The CWT retrieves the time-frequency content information with an improved resolution compared to the STFT. It is the process of wavelet coefficients calculations at every frequency and time point20. The CWT is computed by changing the scale of the analysis window, shifting the window in time, multiplying by the signal, and integrating over all times. It computes the correlation between a wavelet at different scales and the signal with scale (or the frequency) being used as a measure of similarity. In this work Morlet wavelet is used as mother wavelet21. It is a very popular wavelet because of its direct connection between scale and frequency. Morlet wavelets can be reasonably called as time-frequency transform. It is symmetrical, having an explicit expression and providing an exact TFA22. Wavelet scalogram, the squared modulus of the CWT is adopted for time-frequency characterization of fPCG signals. The input of this stage is the segmented fPCG signal, in the form of wave format; whereas outputs are the spectral display for systolic and diastolic parts of the fPCG signal. The results of this implementation are discussed in the following section.
4. Experimental Results:
The signals analyzed in this work have been recorded with the help of DRM. After each recording, the quality of recorded sound is controlled via headphones and monitored by the computer. If the quality of the sound is found low due to ambient noise, recording is repeated. This signal is recorded with a sampling frequency of 8000Hz, 16 bit resolution. The recording is carried out in a quiet room with the assistance of an expert gynecologist. The signal is then de-noised with wavelet based noise suppression procedures23. For this purpose, the fourth order Coiflets wavelet is adopted along with the rigorous SURE threshold de-noising algorithm and soft thresholding rule24. The de-noised signal is then fed as an input to the Simulink model for its segmentation. Application of this fPCG signal to the simulation software, discussed previously, provides five separate outputs of enormous diagnostic importance. These representative outputs are presented and briefly discussed below:
(i) Fetal Phonocardiogram: The fetal Phonocardiogram i.e. fPCG signal is a linear summation of vibrations produced by fetal heart, maternal organs and external sources. These signals are acquired and recorded from the maternal abdominal surface. The fPCG signal carries valuable information about physiological parameters such as fetal heart sound (FHS), fetal heart rate (FHR) and fetal breathing movements25. It is also useful for pre-detection of intra uterine growth retardation and other abnormalities of the unborn26. Figure 5 shows a typical waveform of the fPCG signal for a time span of 4 seconds.
Fig. 5. Typical fPCG Signal
(ii) Envelope of fPCG Signal: The envelope of a signal is the outline that can be realized by connecting all of the peaks in the waveform and it is also termed as envelograph. The envelograph of fPCG signal is generated by creating the analytic signal of the input by using a Hilbert transformer. The envelope of this signal can be found by taking the absolute value of the analytic signal. In order to eliminate ringing and smooth the envelope, the result is subjected to a low-pass filter. The waveform for envelope of fPCG signal is shown in Figure 6.
Fig. 6. Envelograph of the fPCG Signal
(iii) Pulses of fPCG signal: Using threshold technique, rectangular pulses are generated corresponding to each envelope burst. These pulses are of unit amplitude with variable width proportional to the duration of corresponding envelope burst. Figure 7 shows a waveform for the pulses of the fPCG signal.
Fig. 7. Pulses of the fPCG Signal
(iv) Segmentation of S1and S2: The segmentation of fPCG signal is carried out to identify the heart sound components S1 and S2 within the original fetal heart sound. First, the systolic and diastolic periods of the fPCG signal are separated. These separates waveforms of systolic and diastolic periods are then converted into S1s and S2s sequences of the fPCG signal. The results of these steps are depicted in Figure 8.
Fig. 8. Segmented S1s and S2s of the fPCG Signal
(v) Wavelet Scalogram of S1 and S2: Wavelet scalogram communicates the time-frequency localization property of the CWT. The scalogram consists of square of the CWT and represents the percentage of energy for each coefficient. The location of frequency information in the scalogram depends on the wavelet used for the analysis. In this work Morlet wavelet is used for wavelet analysis. The simultaneous display of S1 and S2 scalograms, gives a much better insight of the heart sound characteristic than just a single spectral display of whole cardiac cycle, provided by the conventional methodologies. Figure 9 & 10 shows the scalograms along with three dimensional plots of S1 and S2 segments of the fPCG signal respectively. Where the horizontal axis is time, the vertical axis is scale and the frequency is inversely proportional to the scale value.
Fig. 9. (a) Scalogram & (b) 3-Dim plot of S1s
Fig. 10. (a) Scalogram & (b) 3-Dim plot of S2s
On the basis of above results, it is clear that the CWT is able to resolve both time and scale (frequency) events of the fPCG signal. Scalograms of the segmented fPCG signal show the magnitude of wavelets at various scales as a function of time. The proposed method composed of three stages. First the fPCG signal is converted into corresponding rectangular pulses with variable width proportional to the duration of each envelope burst. Next, the fundamental components (S1 & S2) of fetal heart sound are separated. The segmented S1s and S2s are then used for TFA of the fPCG signal by wavelet scalogram. The scalogram provides energy evolution with time in a single process by viewing a map of the square of the wavelet coefficients. It has the advantage of revealing pockets of high and low energy in different frequency bands. The scale-frequency relationship (established by the WT), and the frequency resolution depends on the wavelet used. The generated results can be effectively utilized for the development of a phonocardiography based fetal monitoring and diagnostic system.
Fetal heart sound (fPCG signal) is an important physiological signal, which contains a large amount of information concerning the pathological status of the fetus. In this paper, TFA of the fPCG signals is performed using wavelet scalogram. These signals are acquired from the maternal abdominal surface using a sensitive and efficient DRM whose working principle is based on passive phonocardiography technique. Separation of S1 and S2 from a complete cardiac cycle of the fetus is carried out through envelope detection and thresholding techniques. Matlab Simulink model is developed for segmentation of the fPCG signals by utilizing the Simulink Toolbox of MatlabTM version 7.8.0 (R2009a). WT based scalogram is adopted for time-frequency characterization of these segmented fPCG signals. Morlet wavelet base function is used for scalogram calculation. It can be concluded from the experimental results that the proposed approach is adequate for analysis of non-stationary and non-linear fPCG signals. The presented method enables to estimate frequency contents in the given fPCG signals. Also, the TFA of segmented fundamental components of the fPCG signal facilitates to estimate their spectral contents separately. The generated information may help in the diagnosing the health status of the fetus as well as for the development of a phonocardiography based fetal monitoring and diagnostic systems.