Iterative FFT-algorithms with high frequency resolution

This paper presents three iterative algorithms for fast Fourier transform with decimation in time; these algorithms have the algorithmic complexity $O(~N~R~\log_2~N)$, where $R$ is the frequency resolution of the spectral characteristic (the ratio of the length of the frequency set to the length of the $N$ set of samples of the source signal). The algorithms differ in the way they organize calculations: some use reverse bit permutation, while the others use additional arrays. Detailed computational graphs and flowcharts of the developed algorithms are provided. The results obtained can be used to improve domestic electronics and software as well as may be included in the training process for engineers in the field of digital signal processing.