much smaller, what influence does the free choice of the arbitrary function / have, and what role does the synthesis function ç that is used to build fh play?
We respond to these questions by introducing a formula for predicting the approximation error in the Fourier domain [BBSS],
(4) Compare f and fh using some norm, for example the mean-square (or L2) norm e2(h) = ||f - Al'2
where f(rn) is the Fourier transform of the arbitrary function f(x) (see Appendix), and where E is an error kernel that depends on the synthesis function only and is given by
It is common practice to impose that ^ be given in a normalized (or scaled) form, such that fo = 1 implies that Co = 1.
Was this article helpful?