ECG Compression - ECG Acquisition and Automated Remote Processing - page 102

Split value of b1 elements b2 - b999 Split value of b1000 elements b1001- b1999 split value of b2000

c1 c 2 c 3 c 4 c1002 c1003 c1004 c1005 c2004 c2005 c2006 c2007

Fig. 5.3 Data grouping illustrated

array c. For next block, element b(1000) will be split and placed as element
c(1003), c(1004), and c(1005). Following, b(1001) to b(1999) will be placed as
c(1006) to c(2004) and so on as illustrated in Fig. 5.3 .
The algorithm steps for generating array c[] from array b[] are provided in End
of Chapter Appendix 1 .
Since the elements in array c[] may either be positive, negative, or even zero, a
suitable sign encoding is now necessary to proceed with further compression
stages. This corresponds to steps III and IV in Fig. 5.2 . The elements of the
generated array c[] are grouped with 8 consecutive elements taken together. The
excess elements (n-h) toward the end of the initial array y are padded with zero
elements. Magnitude and sign encoding are separately performed for each group of
elements, and a new array d[] is generated. Each element in array c[] can be
represented as:

C i ¼ S i : M i ð 5 : 13 Þ

where the sign of ith element C i is represented by S i , which may be +1 or -1, and
Mi represents the absolute value of ith element C i .
The sign elements can be represented with a matrix as follows:

2 3

s 1 s 2 ......s 8
s 9 s 10 ......
............
s n 7 ......s n

4 5

S ¼ ð 5 : 14 Þ

where each row corresponds to the sign information of corresponding group of 8
elements. In sign encoding scheme, the sign of each element in array c[] is rep-
resented by a single bit, with bit '0' ('1') representing positive (negative). Thus, a
single byte in array d[] can be used to represent combined sign information of
corresponding group of 8 elements in array c[]. The encoding rule is:

if S i ¼þ 1 then encoded bit d 8 i ¼ 0
S i ¼ 1 then encoded bit d 8 i ¼ 1

For an example, for eight successive elements c 1 c 2 …….. c 8 = 2, 5, 32, 3, -1,
-3, 0, 0, the corresponding sign elements are given as s 1 s 2 ….. s 8 = [1 1 1 1 -1 -1
1 1].
So, the sign encoded bits are [d 7 d 6 …..d 0 ] = [00001100]= (12) 10.
The magnitude encoding (step IV in Fig. 5.2 ) is performed simultaneously with
sign encoding and grouping operation, for each group of 8 elements of array c[].
Since array c[] deals with positive integers, the magnitude encoding is performed