Part I: Chaos from van der Pol-Duffing Oscillator: Bispectrum Analysis
In part I, it is analyzed the characteristics equation for angular frequency at steady states in the van der Pol-Duffing oscillator, and explained the characteristics of several period limit cycles for different parameters which is occured in the nonlinear stage. Bispectral analysis technique provide us both the theoretical and experimental insight into nonlinear wave process which can not be available from ordinary linear spectral analysis. Bicoherence spectra isolate the mode-mode coupling for period doubling sequence route to chaos of van der Pol-Duffing oscillator will be studied using both bispectrum and bicoherence.
Bispectral analysis techniques were performed on the period-doubling cascade route to chaos for the van der Pol-Duffing oscillator. The calculated period- 1, 2, and 4 states were completely characterized by coherence spectra with interactions between the fundamental frequency and its harmonics. For these three states, the bicoherence spectra provided the degree of nonlinear phase coupling and mode-mode coupling by showing which modes were quadratically interacting.
On the other hand, bicoherence spectra in the chaotic state are diffused all over frequency region so that variousmodes can be excited. Here, although the nonlinear term of van der Pol-Duffing oscillator is cubic rather than quadratic, the bicoherence is found to play an important role to understand the routes from quasiperiodicity to chaotic state for the van der Pol-Duffing oscillator.
Part II: Extraction of Fetal Electrocardiogram(FECG) using Neural Network Based Nonlinear Adaptive Filter
The recording of a fetal electrocardiogram from abdominal surface electrodes is severely obscured by additive noise. There are several sources of interference. As improved technical equipment became available, the detection of waveform of FECG became easier, but the observation of waveform morphology was still difficult because of background noise. The difficulties extracting the fetal electrocardiogram from mother's abdominal ECG signal are mainly the presence of the maternal ECG, the ratively high noise levels, and rather unpredictable configuration of the volume conductor and the bioelectric sources.
A method for removing the mother's electrocardiogram was used to filter the interferences using both linear and neural network based nonlinear adaptive filter. It is demonstrated that the neural network based nonlinear adaptive filter is more useful to predict a nonlinear signal than the linear adaptive filter. Fetal electrocardiogram signals were made by obtaing ECG near heart and abdomen of one adult, and ECG near heart of another adult. It is processed to obtain suitable parameters, ie. step size, number of input taps, number of hidden layer taps, etc., of linear and nonlinear adaptive filters for the above FECG. Fetal electrocardiogram signals from abdominal recordings of real experiments were digitized by A/D converter controlled by a personal computer. Using the obtained parameters, the result of the extracted FECG using nonlinear adaptive filter is more clear, and is higher FECG level than the result using the linear adaptive filter. As conclusion, the nonlinear adaptive filter is more useful to extract FECG from mother's ECG than the linear adaptive filter.