The issues related to the problem of minimizing hardware costs in the digital algorithms’ hardware and software implementation for the discrete signals’ frequency selection on programmable logic devices (PLD) and special processor microelectronic devices are considered. Possible ways to solve these problems are described based on the computational algorithms for non-recursive digital filtering (NDF) and difference digital filtering with integer coefficients use. A necessary and sufficient condition is given for using a computational algorithm’s hardware and software implementation of discrete signals’ difference digital filtering for their multi-stage discrete Fourier transform without performing arithmetic multiplication operations.

The issues related to the digitalization of the spectral analysis of the polyharmonic signal are considered. There are various digital methods of discrete Fourier transform (DFT) of such a signal. The purpose of the study is a comparative analysis of the known methods for transforming a complex signal, which make it possible to minimize the required number of multiplication operations in its transformation algorithms. The research used methods of mathematical and software modeling of digital signal processing algorithms. The methods of discrete Fourier transform based on multiband digital filtering (MDF) with one low-frequency digital filter and with an extended window based on the so-called bank of non-recursive digital filters (BDF) are described. There are the results of a comparative analysis of these methods.

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