Dealiasing of the spectra of sampled noise

Noise power spectra gained through discrete Fourier transform of sampled noise show the effects of aliasing and filtering at all frequencies, whatever the sampling rate and the filter cut-off frequencies. A self consistent method for the necessary correction of the spectra is developped, given the filter response. It is first shown that, with RLC filters, the uncorrected spectrum of white noise and 1/f - noise can be represented by Digamma functions, Polygamma functions, or by corresponding integrals. In certain cases the correction function can be calculated in simple form, and an example of dealiasing and defiltering of white noise is given. Finally, estimates of the truncation error of the sums representing the uncorrected spectra are given. In general, the spectra can be reconstituted all the way up to the folding frequency with tolerable computational effort.