Some alternate realizations of the arithmetic Fourier transform

This paper presents some alternate methods to realize the arithmetic Fourier transform (AFT). Method one uses recursion to remove the need for the Mobius function. Method two modulates the input signal with a cosine wave to remove the need for the Mobius function. Method three integrates the input signal to eliminate the divisions inherent in the AFT. Delta-modulation and the integration method are combined to produce a multiplier free structure for realizing the AFT. The performance of these methods are compared.<>