Data extensions and their effects on the DFT results

1D DFT algorithms receive as input a 1D array of

N

complex numbers (say, samples of a given continuous complex- or real-valued function

y

=

g

(

x

)), and return as their output a 1D array of

N

complex numbers which contains the discrete frequency spectrum. However, when the result obtained by DFT with

N

data values is not yet satisfactory, one may wonder if a larger number of data values could improve the results. In fact, there exist several possible ways to extend the input data for the DFT, each of which yields quite different results. In this appendix we examine 6 of the most simple ways of extending the input data, and explain how they influence the DFT results (including the possible effects on the DFT artifacts). As we will see, some of these 6 methods are indeed useful and advantageous, depending on one’s aims and also on the nature of the data, while others are rather misleading and may introduce significant artifacts. Note that although the discussion in this appendix is presented for the 1D case, its generalization to 2D or MD DFT is straightforward.