Discrete-time modeling of polynomial-based interpolation filters in rational sampling rate conversion

Abstract

If sampling rate conversion (SRC) is performed between arbitrary sampling rates, then the SRC factor can be a ratio of two very large integers or even an irrational number. An efficient way to reduce the implementation complexity of a SRC system in those cases is to use polynomial-based interpolation filters that mimic digitally the hybrid analogue/digital system. In practice, the sampling rate conversion is approximated with a rational factor. In this case, the hybrid analogue/digital model used to represent the SRC process may be represented by an equivalent discrete-time model. The discrete-time modeling of the rational SRC has been used earlier for the zeroth order interpolation. This paper extends this idea to arbitrary polynomial-based interpolation. Furthermore, this paper derives the relation between various polynomial-based interpolation filters (Farrow structure and its modifications) and polyphase FIR model filters. This paper observes possible applications of these relations, such as filter design, implementation complexity reduction, and response distortion analysis.