%0 Journal Article %1 Cooley1969Finite %A Cooley, J. %A Lewis, P. %A Welch, P. %B Audio and Electroacoustics, IEEE Transactions on %D 1969 %J Audio and Electroacoustics, IEEE Transactions on %K ft %N 2 %P 77--85 %T The finite Fourier transform %U http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1162036 %V 17 %X The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.

@article{Cooley1969Finite, abstract = {{The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Cooley, J. and Lewis, P. and Welch, P.}, biburl = {https://www.bibsonomy.org/bibtex/2a6797d16ee8402486a4a0811b0d360b5/nonancourt}, booktitle = {Audio and Electroacoustics, IEEE Transactions on}, citeulike-article-id = {3906643}, citeulike-linkout-0 = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1162036}, interhash = {365566569285fb05dfc030e0c62b9a6b}, intrahash = {a6797d16ee8402486a4a0811b0d360b5}, journal = {Audio and Electroacoustics, IEEE Transactions on}, keywords = {ft}, number = 2, pages = {77--85}, posted-at = {2009-01-19 00:24:11}, priority = {2}, timestamp = {2019-06-10T14:53:09.000+0200}, title = {{The finite Fourier transform}}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1162036}, volume = 17, year = 1969 }