ABSTRACT
S. Nikolopoulos,1 P. Kapiris,2 K. Karamanos3 and K. Eftaxias2,a 1National Technical Univ. Athens, Dept. of Electrical & Computer Engineering Zografou Campus,
2, , r-x -x , 1
i j i C m r
N τ
⎡ ⎤= Θ ⎣ ⎦− ∑ ∑ (A3) where xi and xj are as in Eq. (8). Θ is the Heavyside function:
( ) ( ) ( ). 1, x i -x j
no of j N m such that r C i
N m
⎡ ⎤≤ − − ≤⎣ ⎦= − − (B2)
( ) ( ) ( )1, lim .m mNApEn m r r r+→∞ ⎡ ⎤= Φ −Φ⎣ ⎦ (B4) It is therefore found that ( ) ( )rrApEn mm Φ−Φ=− +1 and is equal to the average over
,
1 1ln ln
1 ln ln
ln1 ln
ApEn m r r r
C i C i N m N m
C i C i N m
C i N m C i
− = Φ −Φ
⎡ ⎤ ⎡ ⎤= −⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦
⎢ ⎥≈ −⎣ ⎦−
= −
