On implementing the arithmetic Fourier transform

The arithmetic Fourier transform (AFT), a method for computing the Fourier coefficients of a complex-valued periodic function, is based on a formula which has the advantage of eliminating many of the multiplications usually associated with computing discrete Fourier coefficients, but has the disadvantage of requiring samples of the signal at nonuniformly spaced time values. A method for computing the Fourier coefficients which allows uniform sampling at arbitrarily chosen sampling rates is developed. The technique still requires few multiplications, albeit at the expense of a limited amount of linear interpolation of the sample values. Efficient hardware implementations of this algorithm are presented.<
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