The comprehensive description of Multidimensional Fourier Transform applied to arbitrary sampled NMR data is presented. Lineshapes and signal-to-artifact ratio are discussed in detail with regard to time domain sampling scheme and applied data weighting. It is demonstrated that transformation method with simple summation instead of numerical integration is most useful for significantly undersampled experiments. Additionally, the optimized random sampling schedule which enables significant improvement of obtained spectra is proposed. The new procedure of cleaning spectra is presented, it is based on predictability of artifacts pattern when sampling scheme and amplitude of intense signals are known. The results enable observation of high dynamic range spectra as for example heteronuclear edited NOESY. We show the application of new approach to the 3D (15)N-edited NOESY-HSQC spectrum acquired for (13)C, (15)N labeled ubiquitin sample with random time domain sampling.