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Figure 2. Multiple generated IWCs by the mathematical model. Changing the parameters can generate various forms of IWC at different frequencies and intensities. The periodicity of the IWCs can also be controlled.

Figure 3. IWCs with local minimums and maximums identified.

Figure 4. Envelop Estimation using the Hilbert Transform.

Figure 5. Two IWCs with the selected points for parameter extraction identified. The turning points are identified to facilitate the reconstruction procedure. The minimum and maximum turning points help determine the shape of the curve at these locations.

Figure 6. Generated and reconstructed Individual Wave Components. The algorithm reproduces the IWCs correctly up to a small amplitude difference.

Figure 7. Amplitude error signal between the original and reconstructed IWC. The error follows the shape of the Individual Wave Component. The amplitude level shows a small error in the reconstruction process.

Figure 8. Spectrograms showing bowel sound recordings. In both plots, the individual wave components are identified. The top figure shows the spectrogram of the original recording. The bottom figure shows the spectrogram of the reconstructed signal of the first

Figure 9. Human digestive system with all four quadrants identified.

Figure 10. Time-domain bowel sound signals of two different states of the digestive system. The top figure represents a recorded bowel sound signal when water enters the stomach. The bottom figure represents a bowel sound generated by a patient with an empty stomach.

Figure 11. Spectrograms of recorded bowel sounds from a patient with an empty stomach. The top figure is the original recorded bowel signal. It shows a lot of activities once the bowel movement starts. The bottom figure shows the reconstruction of a series of indi vidual wave components. The echo signals from the main individual wave components bounce against the digestive system’s empty wall, creating more individual wave components but at a lower intensity.

Figure 12. Spectrograms of recorded bowel sounds from a patient with an empty stomach. The top figure is the original recorded bowel signal. It shows a lot of activities once the bowel movement starts. The echo signals from the main individual wave components bounce against the digestive wall.

Figure 13. Recorded clinical bowel sound signal in a noisy environment.

Figure 14. The complete extraction process. The envelope is obtained using the Hilbert transform of the IWC, and the red and black points are selected for curve-fitting.

Figure 15. Original and reconstructed IWCs. The reconstructed bowel sound signal maintains the shape and features of the original.

Figure 16. Root Mean Square Error (RMSE) of an IWC. We average over 500 iterations per SNR value.