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The arithmetic Fourier transform (AFT) is an important Fourier analysis technique. Since AFT algorithms require lots of non-uniform samples, zero-order interpolation is used for implementing AFT, but this method can produce significant errors. To reduce the errors, over-sampling is needed, meaning the sampling rate should be a number of times the Nyquist rate. The over-sampling problem is the main drawback of AFT. In this paper a new method for implementing AFT with no need for over-sampling is presented. This method gains nearly the same effect as the method using over-sampling, so it makes it possible for us to implement AFT with sampling at the Nyquist rate.