The mappings from one-dimensional data series into multidimensional array

in which the lengths of every pair of dimensions are relatively prime

are the basis of the Wino-grad Fourier Transform Algorithm （WFTA）. This paper presents a general formulation of index mappings for L-dimensional DFT from one-dimensional DFT and shows that the possible numberof these mappings is L

where φ（ · ）is the Euler function

as for each mapping the transform formulations are given. An example shows that there are several particular mappings whose input and output index mapping are identical when N = 4·5 = 20.Some doubts have been raised about the results obtained by Kolba

Parks[5] and Winograd[6] in discussing the special case L = 2.In sectionV of [5] expressions r1 = M2 （mod M1）

r2 = M1 （mod M2） should be written as r: M2=1 （mod M1）

r2 M1 =1 （mod M2）. In Section IV of [6]

formulations for the index mapping （mod n） and Bk1n2+k2=As1k1n1+s2k2n2 （mod n）

should be replaced by either

（mod n） and Bk1n2+k2=As2k1n2+s1+k2+n1 （mod n） or bj1n1+j2=ar1j1n1+r2j2n2 （mod n） and Bk1n1+k2=As1k1n1+s2k2n2 （mod n）.At 1979 IEEE Int’l Conf. on ASSP

the paper[8] by Ellioff and Orton presented the same view as this article

even though the case of general L was discussed

and the formulations ofindex mappings were only meant for two particular cases of .