MATHEMATICAL DESCRIPTION AND ALGORITHMS FOR THE IMPLEMENTATION OF DIGITAL FILTERS

This article presents a generalized model for developing infinite and finite impulse characteristics digital filters, as well as discusses their possible implementation in electronic information processing systems. Particular attention is paid to the spectral representations of such filters in complex frequency coordinates. The presented algorithms allow for the efficient calculation of the real and imaginary parts of the instantaneous signal spectrum at a given frequency using digital filters. The proposed method for analyzing filter performance in steady-state and transient modes based on the Laplace transform requires significantly fewer computational resources compared to traditional approaches, such as the application of the expansion theorem.