  For precise QCD prediction of observables, the ambiguity due to renormalons
in perturbative calculations should be appropriately separated from Wilson
coefficients in the framework of the operator-product-expansion. Recently, a
new method has been developed which utilizes the properties of Fourier
transform to separate multiple renormalons simultaneously from the Wilson
coefficients. To understand how this method works analytically, we perform a
renormalon separation from various toy models with the one-loop beta function.
We confirm that each of the results is consistent with the theoretical
expectations. In addition, we present a new formula for the resummation of UV
renormalons and study its validity using one of the toy models.
