# THE NUMBER OF POLYNOMIAL SEGMENTS AND THE POLYNOMIAL ORDER OF POLYNOMIAL-BASED FILTERS

## Keywords:

Decimation, Estimation formula, Farrow structure, Interpolation, Polynomial-based interpolation filters## Abstract

Many digital signal processing applications can benefit from polynomial-based interpolation filters based on the Farrow structure or its variations. The number of polynomial segments determining the finite length of the filter impulse response and the order of polynomials in each polynomial segment are the two main design parameters for these filters. These parameters are linked to the complexity of the implementation structure and frequency domain performance. As a result, determining the value of these two parameters based on system requirements is beneficial in order to estimate complexity of the filter, and starting values for a design. This paper offers formulas for estimating the length and polynomial order of polynomial-based filters for a variety of criteria, including stopband attenuation, transition bandwidth, passband deviation, and passband/stopband weighting.

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*REVUE ROUMAINE DES SCIENCES TECHNIQUES — SÉRIE ÉLECTROTECHNIQUE ET ÉNERGÉTIQUE*,

*66*(3), 187-190. https://journal.iem.pub.ro/rrst-ee/article/view/24