Mathematical analyses of artifacts which are difficult to avoid in a conventional data processing of correlation NMR are given. In the discrete Fourier transformation, which is used in the digital processing, it is tacitly assumed that a sequence of data is periodic. When the baseline is tilted, the first and the last points of the sequence are different in magnitude, and therefore a discontinuity results in the sequence. In the digital Fourier transformation of this type of sequence, the truncation error becomes considerable, resulting in a severe baseline oscillation in the correlation NMR spectrum. In the limit of the zero sweep rate, this type of oscillation is equivalent to the Gibbs phenomenon which is well known in the theory of Fourier series. A mathematical basis for the wing processing, which we have previously proposed, is given. Another advantage of wing processing is that signals which exist outside the frequency range covered by the sweep but give a residual ringing in the rapid scan response can correctly be recognized as such, and the aliased lines do not appear and disturb the NMR spectrum of interest.