343 
Operator 
Function 
GLOBAL 
FOURIER-Transformation 
exp t (x) 
WALSH -Transformation 
wal s (K) 
HAAR -Transformation 
har^ n ^(K) 
LOCAL 
function value on the 
digitizing place 
sin X 
HARDY-function 
X 
interpolation in a neigh 
bourhood (integration) 
rect x 
interpolation with 
polynomes +) 
(rect x) * (rect x) * ... 
E. g. for the cubuic SPLINE-interpolation the characteristic 
function is (rect x) * (rect x) * (rect x) 
Table 1: Function systems for transformations 
(I) 
data structure 
changing 
(II) 
data structure 
preserving 
Mathematical 
background 
Where , N Whe re to ? 
from ? c —> ‘ 
How ? 
Table 3: Mathematical background of transformations