By Cong, Fengyu; Lyytinen, Heikki; Ristaniemi, Tapani
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Additional info for Advanced signal processing on brain event-related potentials : filtering ERPs in time, frequency and space domains sequentially and simultaneously
Mallat first proposed this idea (Mallat, 1989). 5 Mother wavelet and shifted mother wavelet. The above example is a Meyer wavelet. March 4, 2015 5:46 Advanced Signal Processing on Brain ERPs 9 x 6in Wavelet Filter Design Based on Frequency Responses b1907-ch02 page 25 25 length-T discrete sequence x(t) (t = 0, 1, 2, . . , T − 1) is expressed as DWT(n, m) = √ 1 |2n | T −1 x(t)ψ t =0 t − 2n · m , 2n (2-9) where a and b in the CWT are replaced by 2n and 2n · m, respectively; n and m are integers.
2005). An Introduction to the Event-Related Potential Technique Cambridge, MA: The MIT Press. , Jung, T. , Bell, A. , & Sejnowski, T. J. (1997). Blind separation of auditory event-related brain responses into independent components. Proceedings of the National Academy of Sciences of the United States of America, 94(20), 10979–10984. , Hansen, L. , & Arnfred, S. M. (2007). ERPWAVELAB a toolbox for multichannel analysis of time-frequency transformed event related potentials. Journal of Neuroscience Methods, 161(2), 361–368.
9 Examples of the impulse responses of the wavelet filters (the coefficients at several levels are used for the signal reconstruction). (a) Unit impulse. (b) Impulse response. The duration of the unit impulse is 1400 ms (−700 to 700 ms). The sampling frequency of the unit impulse is 1000 Hz, and the number of levels for the decomposition is 10 according to Eq. (2-11). The coefficients at levels #9, #8, #7, and #6 are used for signal reconstruction. 10 Examples of the magnitude responses of the wavelet filters (the coefficients at several levels are used for the signal reconstruction).