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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Issues related to aliasing
verfasst von : Isaac Amidror
Erschienen in: Mastering the Discrete Fourier Transform in One, Two or Several Dimensions
Verlag: Springer London
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When the DFT is used as a numerical approximation to the Fourier transform of an underlying continuous function, some differences can be expected between the two. For example, it is clear that the DFT can only give us the Fourier transform values at the N discrete points for which the computation is done. However, even at these points there may appear in some cases quite significant discrepancies, in spite of the adjustments and scalings discussed above in Chapters 3 and 4. This is not a result of rounding errors in the calculations, which are normally quite insignificant (see Sec. 8.8). The main reason for these discrepancies resides in the discrete and finite nature of the DFT, which implies that the underlying continuous function must be sampled, and that it can only be considered within a finite range.