We improve on Fourier transforms (FT) between imaginary time $tau$ and imaginary frequency $omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Greens function can be improved by using a sumrule boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part.
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