Design of polynomial-based digital interpolation filters based on Chebyshev polynomials

摘要

Polynomial-based digital filter is a very effective tool for realization of the programmable digital filters. The fundamental concept for the polynomial filters is to express their impulse response, or filter coefficients as a piecewise polynomial function of the parameters that have to be adjusted, resulting in an efficient realization, so called the Farrow structure. In this contribution, Chebyshev polynomials are used as basis functions to construct a piecewise polynomial impulse response. The polynomial coefficients can be optimized directly in the frequency domain. The minimax optimization method is generalized and modified in order to design polynomial-based interpolation filters based on Chebyshev polynomials. We show that the performance of polynomial based filter in frequency domain cannot be changed whatever polynomial kernel is used.