[math-fun] What's this operation called?

Given an n-dimensional vector v over a field K, and a basis such that all the components are nonzero. (Or over a ring R, and all the components are units.) Take the componentwise inverse to get v'; next, multiply componentwise by a nonzero row of the n-dimensional FFT to get v''. Has anyone seen this before? Does it have a name? -- Mike Stay staym@clear.net.nz http://www.cs.auckland.ac.nz/~msta039