Adsorption energy distributions from experimental gas adsorption isotherms are capable to characterize the energetic heterogeneity of a solid surface. Unfortunately, they can only be computed by the adsorption integral equation, which represents an ill-posed problem, i.e., the solution is highly sensitive to errors in the input data. Ill-posed problems are usually solved by means of regularization, but general regularization schemata do not provide useful criteria to estimate the approximation quality. In this paper, a former presented solution strategy tailor-made for the Langmuir kernel of the adsorption integral equation is extended to Fourier transform. This yields a simple and effective cutoff criterion for the Fourier cosine transform of the adsorption energy distribution. The cutoff criterion is applied to calculate adsorption energy distributions from synthetic and experimental adsorption isotherms.