BIFORE phase spectrum and the modified Hadamard transform

A fast method for calculating the BIFORE phase spectrum for different circular shifts of the input data is developed. A simple relationship between the BIFORE phase spectrum and the modified Hadamard transform (MHT) coefficients is established. It is also pointed out that given the BIFORE power spectrum and the phase spectrum for circular shifts of 0 to (N/2 - 1), the input data can be reconstructed.