Ii2

much smaller, what influence does the free choice of the arbitrary function / have, and what role does the synthesis function รง 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.

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