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A generalized technique for the reconstruction of permittivity profiles in an arbitrary coordinate system is presented. The resolution of the reconstructed permittivity profile can precisely be controlled by adjusting the ratio between the bandwidth and the midband frequency of frequency-dependent measured data, or equivalently the duration of a pulse modulated carrier used to produce time-dependent measurements. The proposed technique represents in fact a versatile relaxation of the well-known Fourier transformation method used to reconstruct one-dimensional profiles in half-spaces or slab-shaped media in Cartesian coordinate systems. Representative cases in the Cartesian coordinate system have been considered for validating the suggested technique. Excellent agreement between the original and reconstructed permittivity profiles has been achieved.