  G. Anderson and B. Farrel showed that conjugation of constant matrices by
asymptotically liberating random unitary matrices give rise to asymptotic free
independence. Independent Haar-unitary random matrices and independent
Haar-orthogonal random matrices are examples of asymptotically liberating
ensembles. In this paper, we investigate the fluctuation moments, and higher
order moments, induced on constant matrices by conjugation with asymptotically
liberating ensembles. In particular, we determine fluctuation moments induced
by an ensembles related to the Discrete Fourier Transform matrix.
