The optimal transform for the discrete Hirschman uncertainty principle

We determine all signals giving equality for the discrete Hirschman uncerta inty principle, We single out the case where the entropies of the time sign al and its Fourier transform are equal, These signals (up to scaler multipl es) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal, The transform may be compute d via a fast algorithm due to its relationship to the discrete Fourier tran sform.