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BIFORE or Hadamard transform is defined and several of its properties are developed. BIFORE power and phase spectra are developed and their frequency-sequency composition is explored. Using matrix partitioning, fast algorithms for efficient computation of BIFORE coefficients and power and phase spectra are developed. Multidimensional BIFORE transform is defined and a physical interpretation of its power spectrum is presented. Advantages and as well the limitations of the BIFORE transform in its application in information processing are cited.