Tham khảo tài liệu 'recent advances in biomedical engineering 2011 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Compression of Surface Electromyographic Signals Using Two-Dimensional Techniques 29 If we denote the position vectors v1 and v2 by their respective pair of discrete coordinates m n and j i respectively then the autocorrelation function can be expressed as Rx n m i j Rx n - i m - j Rx i - n j - m . 6 If we use the discrete variables k and r to denote the coordinate differences n-i and m-j respectively the above equation can be rewritten as Rx n m i j Rx k r Rx -k -r . 7 In general the autocorrelation function of a random field is a function of four variables. However the autocorrelation function of a homogeneous random field . S-EMG data is a function of only two variables k and r N-1M-1 Rx k r E x n m x n k m r 2 2 x n m x n k m r . 8 n 0 m 0 The autocovariance function Cx k r is defined as N-1M -1 Cx k r E x n m x n k m r - p2 22 x n m x n k m r - p . 9 n 0 m 0 Under the assumption that a class of rearranged S-EMG data forms a homogeneous random field the autocorrelation function Rx k r may be assumed to be of the form Rx k r Rx 0 0 - p2 e- -M p2 10 where a and p are positive constants Rosenfeld Kak 1982 and where by definition 2 N-1M-1 2 Rx 0 0 e x n m 2 2 x n m and n 0 m 0 1 N-1 M-1 p E x n m -22x n m 0 . NM n 0 m 0 For rearranged S-EMG data p 0 and the autocorrelation function is reduced to Rx k r Rx 0 0 e-w-M Cx k r . 11 12 13 Constants a and p can be distinct due to the nature of rearranged S-EMG data. This means that the autocorrelation function can be used to model two-dimensional data with different degrees of correlation in the horizontal and vertical directions by specifying the values of a and p. In our method one direction corresponds to linear time data sampling with strong 30 Recent Advances in Biomedical Engineering correlation and the other corresponds to window step and leads to weak correlation. The correlation along the window step direction may be increased using column reordering based on inter-column correlation as discussed in the next .
