6. Discussion and Conclusion
6.6 Future Work
Research in meditation is still in its infancy. Human body is a delicate and magnificent ‘sensor’ capable of perceiving subtle effects produced by meditation, to such a scale that even scientific technology falls far behind. One of the most important issues concerns the access to actual knowledge of meditation state. At current stage, we mainly rely on post-recording interview. Sophisticated experimental protocol is required to gain access to meditation state without interfering with the meditation course.
Microstate analysis provides a framework for relating the microscopic properties
of small group of neurons to the macroscopic or bulk properties of larger cerebral region, therefore, explaining brain dynamics of Zen meditation in totally different and pioneering aspect at the microscopic level. Future research can be devoted to the analysis of Zen-meditation microstate.
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Appendix
The discrete wavelet transform (DWT) of a signal x is calculated by passing it through a series of filters. First the samples are passed through a low pass filter with impulse response g resulting in a convolution of the two:
[ ] ( ) [ ] ∑
∞[ ] [ ]
The signal is also decomposed simultaneously using a high-pass filter h. The outputs giving the detail coefficients (from the high-pass filter) and approximation coefficients (from the low-pass). The two filters are related to each other and they are known as a quadrature mirror filter.
However, since half the frequencies of the signal have now been removed, half the samples can be discarded according to Nyquist’s rule. The filter outputs are then downsampled by 2:
Here is the schematic diagram with a real signal inserted into it.
[ ]
nyhigh 500 data points
[ ]
n x1000 data points ylow
[ ]
n 500 data pointsFig. A-1: The scheme diagram of the low-pass and high-pass filter
Here the output is the high frequency DWT coefficients cD, and
is the low frequency DWT coefficients cA. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components. This is called the
[ ]
n yhigh[ ]
n ylowwavelet decomposition tree. Below is the wavelet decomposition tree we used in chapter 5.
Fig. A-2: The wavelet decomposition tree
To calculate the power of each frequency band, we reconstruct the signal by assembling these coefficients back without any loss. Below is the process of decomposition and reconstruction
Fig. A-3: The process of decomposition and reconstruction
a0 (0-512Hz)
a1 (0-256Hz) d1 (256-512Hz)
a2 (0-128Hz) d2 (128-256Hz)
a3 (0-64Hz) d3 (64-128Hz)
a4 (0-32Hz) d4 (32-64Hz)
a5 (0-16Hz) d5 (16-32Hz) Beta
a6 (0-8Hz) d6 (8-16Hz)
a7 (0-4Hz) Delta d7 (4-8Hz) Theta da7 (8-12Hz) alpha dd7 (12-16Hz)
S
H H'
L L
S
The low- and high-pass decomposition filters (L and H), together with their associated reconstruction filters (L' and H'), form a system of what is called quadrature mirror filters.
We pass the coefficient vector cA1 through the same process we used to reconstruct the original signal. However, instead of combining it with the level-one detail cD1, we feed in a vector of zeros in place of the detail coefficients vector:
H'
Fig. A-4: The process of reconstructing the low frequency component L
The process yields a reconstructed approximation A1, which has the same length as the original signal S and which is a real approximation of it.
Similarly, we can reconstruct the detail D1, using the analogous process:
H'
Fig. A-5: The process of reconstructing the high frequency component L
The reconstructed approximations and details are constituents of original signal.
We utilize this method to reconstruct the level we are interested, and then calculate the power of it.
Vita and Publication List
Chuan-Yi Liu received his B.C. degree in Electrical Engineering from National Taiwan University of Science and Technology, Taiwan in 1997 and Ph D. degree in Electrical and Control Engineering from National Chiao-Tung University, Taiwan in 2007. His research interests include biomedical signal processing, electrophysiological phenomenon, and pattern recognition and classification.
Journal:
1. CY Liu, CC Wei and PC Lo, “Variation Analysis of the Sphygmogram to Assess the Cardiovascular System under Meditation”, Evidence-based Complementary and Alternative Medicine (Accepted)
2. HC Liao, CY Liu and PC Lo, “Investigation of Visual Perception under Zen-Meditation based on Alpha-dependent F-VEPs”, Journal of Biomedical Engineering Research, Vol. 27, No. 6, pp. 384-391, 2006
3. CY Liu and PC Lo, “Spatial Focalization of Zen-Meditation Brain Based on EEG”, Journal of Biomedical Engineering Research (Accepted)
4. CY Liu and PC Lo, “F-VEPs in Zen meditation”, Biomedical Engineering-Applications, Basis and Communications (Accpted)
Conference:
1. Liu CY and Lo PC, "Flash-VEP in Meditation", International Symposium on Biomedical Engineering (ISOBME), Tainan, Taiwan, Dec 17-18, 2004
2. Chang KM, Liu CY and Lo PC, "An investigation of inner light during Zen meditation using alpha-suppressed EEG and VEP", 2nd International IEEE EMBS Conference on Neural Engineering, Washinton DC, USA. March 16-19, 2005, On page(s): 656- 659
3. Liu CY and Lo PC, "Flash Visual Evoked Potentials in Zen-Buddhist Meditation", 3rd European Medical & Biological Engineering Conference (EMBEC 2005), Prague (Czech Republic), Nov 20-25, 2005
4. Lin JD, Liu CY and Lo PC, "Evaluate the Effects of Meditation using Bioacoustic Vocal Profiling", International Symposium on Biomedical Engineering (ISOBME), Taipei, Taiwan, Dec 15-16, 2006
5. Liu CY and Lo PC, "Investigation of Spatial Characteristics of Meditation EEG Using Wavelet Analysis and Fuzzy Classifier", The 5th International Association of Science and Technology for Development (IASTED) Conference on Biomedical Engineering, Innsbruck, Austria, Feb 14-16, 2007