tailieunhanh - New Developments in Biomedical Engineering 2011 Part 4

Tham khảo tài liệu 'new developments in biomedical engineering 2011 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 112 Recent Advances in Biomedical Engineering Suppose there are L sessions performed. Let yi t where sessional index i 1 2 . L be the response to equispaced stimuli hi t the corresponding SOA is denoted as Ti and x t be the transient response to an individual stimulus assumed identical for sessions then yi t hi t x t as derived before. This model can also be expressed in matrix operation . yi mix where binary matrix mi is constructed by circular-shift versions of hi t in step-wise fashion. The row size of mi is user defined which is at least larger than the length of x t . This process is the same as Eq. 7 except that hi t is equispaced. Ideally yi t is supposed to be a periodic steady-state response due to overlapping. By carrying out conventional ensemble averaging gives one period of the overlapped response yi t t e 0 Ti . This is equivalent to keep the column size of mi to be Ti. A sweep-like response y t is formed by concatenating individual yi t one by one together y t yi t y2 t . y t Mx t 16 where M mi m2 . mL . By applying the pseudo-inverse matrix M-1 x t can be retrieved. An illustration of this process is shown in Fig. 4. Note that the use of this method must be taken with care for the lack of discussions on noise effects. In fact any matrix inverse calculation in practice might suffer the ill conditioning problem which is very sensitive to tiny disturbance. A B T1 T2 T3 T4 T5 T6 T7 T8 time Fig. 4. The Simulation of session-jittering deconvolution. A Eight sessions of responses yi t concatenate one by one according to a ascendant order of Ti. Ti Ts corresponding to SOAs increasing with a constant step-size represent length of individual yi t . B Recovered response dotted line obtained by deconvolution is identical with original response solid line . 3. Recoding efficiency with high rate stimulation Given the same number of stimulus people expect that high rate stimulation would reduce the recording time and the signal to noise ratio SNR for high rate