A : Derivations of results
نویسندگان
چکیده
respectively. In either case, choosing α̂(ω) = δ(ω) results in a variance proportional to that of the integrand. These equations provide different insight into the choice of importance function for variance reduction. Eq. 2 suggests that ideally, g(x) = 1/α(x) should be chosen so that α̂(ω) contains all its energy at frequencies where the square of the integrand has no energy. Eq. 3, on the other hand implies that the ideal situation is when (f̂Π ⊗ α̂)(ω) = δ(ω), or that the weighting function warps the integrand into a constant.
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