Digital Signal Multi-Stage Discrete Fourier Transform and Its Practical Applications

The issues related to the study of the problem of minimizing hardware costs for software and hardware implementation of algorithms for frequency selection of digital signals on programmable logic devices are considered. The purpose of the study is to define the theoretical foundations of the concept and methodology of the multi-stage discrete Fourier transform without performing multiplication operations. The methods of software and hardware modeling of digital signal processing algorithms were used in the study. The principles of the multi-stage discrete Fourier transform of complex signals are specified only by the operations of adding their time samples. Its methods and digital algorithms are presented. Their basic formulas are given.