How the Discrete Hirschman Transform Inherits its Eigenstructure from the DFT.

Following the earlier work, the discrete Hirschman transform (DHT) structure is extended to other transforms: the cosine, sine, Walsh-Hadamard and the wavelet transforms. The eigenstructure of the discrete Hirschman transforms are derived, and in fact we show that they are inherited directly from the DFT eigenstructure. Two properties of the discrete Hirschman transforms, invertibility and unitarity, are proven.