Spectral estimation by AFT computation

At the beginning of this century Bruns developed a method for computing the coefficients of the Fourier series of a periodic function y(t) using the Möbius inversion formula. This idea for Fourier analysis was considered again by Wintner from an arithmetical point of view in 1945. In recent papers, many authors have shown that the arithmetic Fourier transform (AFT) computation is more convenient in signal processing, requiring a reduced computation load, than are fast Fourier transform and convolution algorithms. The data dependence in the AFT is not uniform (this algorithm requires nonequidistant inputs to produce equidistant spectral coefficients). To have a series of suitable values as AFT inputs, oversampling or interpolation is used. In these papers, bases on algorithms, evaluations of errors in the spectral coefficients computation using AFT, and the complexity of different hardware and software solutions for the AFT computation are proposed. The spectral coefficients computed via AFT and via discrete Fourier transform are compared in terms of accuracy. AFT computation proves to be an easy task but its software or hardware implementation is much more complex. Furthermore there is not a complete evaluation of AFT in any of the papers. Our aim is to provide a complete evaluation of this algorithm.