Evaluation of Frequency Characteristics Approximation Error at the Output of Fir-Filter Calculated by Parks-Mcclellan Algorithm

Abstract

A method for designing a high-order FIR filter calculated by the Packs-McClellan algorithm is considered in the paper. It is shown that the reasons for the limited order of the filter are errors describing Chebyshev polynomials arising from the discrete representation of polynomials. The separation of the projected filter into cascades of the same order allows to ensure the optimal construction of the filter while maintaining the linearity of its phase-frequency characteristics. The estimates of the errors of approximation of the amplitude frequency response of the filter in case of its cascade implementation are given. It is shown that the method of designing a filter made as a cascade connection is simplified compared to designing a high order filter; the amount of memory allocated for storing filter coefficients decreases, the approximation error in the retention band decreases, but the approximation error in the passband increases in proportion to the number of stages.