Abstract

A signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signal. The signal processing apparatus and method utilize a process in which a data set of samples is used to iteratively compute a set of frequency samples, wherein each computational iteration utilizes error information which is calculated between the initial data and data synthesized using the AFT. The iterative computations converge and provide AFT values at the Farey-fraction arguments which are consistent with values given by a zero-padded Discrete Fourier Transform (DFT), thus obtaining dense frequency domain samples without interpolation or zero-padding.