Weighted finite automata (WFA) have been introduced as devices for com
puting real functions on [0,1](n). The main motivation has been to gen
erate functions on [0,1] x [0,1] interpreted as gray-tone images. Weig
hted finite transducers (WFT) are finite state devices that serve as a
powerful tool for describing and implementing a large variety of imag
e transformations and more generally linear operators on real function
s. Here we show new results on WFT and demonstrate that WFT are indeed
an excellent tool for image manipulation and more generally for funct
ion transformation. We note that every WFA transformation is a linear
operator and show that most of the interesting linear operators on rea
l functions (on [0,1](2)) can be easily implemented by WFT. We give a
number of examples that include affine transformations, a low-pass fil
ter, wavelet transform, (partial) derivatives, simple and multiple int
egrals. Since the family of WFA-functions is constructively closed und
er WFT, each of our examples is actually a proof of a theorem stating
that for each WFA A there effectively exists another WFA B that comput
es the integral (or other transformations) of the function defined by
A.