Given a unitary matrix U which I know there exists a unitary diagonal matrix D (unit circle elements in diagonal) such that DFT2(UD) is diagonal (i.e there exists another unitary diagonal matrix V such that V=FUD(F^H) whee F is the fourier matrix)
Is there a way of finding D or V?
If the answer is yes, is it also possible for rectangle matrix U with NxM (N>M) where U's columns are orthogonal?
Thanks in advance