Polynomial-based filters with polynomial pieces of different lengths for interpolation

This contribution presents an idea of polynomial-based filters with segments of different lengths which can be effectively used for sampling rate conversion. For these filters the impulse response is characterized by the following: in each interval of length T_n the impulse response is expressed as polynomial of low order M, there are all together N intervals, and the impulse response is symmetric around its middle point. In the case of interpolation (decimation), the length of every polynomial segment can be arbitrary integer multiple of input (output) sampling period. In this paper, the effective implementation structure for these filters is derived. The implementation structure is based on the known Farrow structure which is commonly used for implementation of various types of polynomial-based filters. It is also shown that the number of fixed coefficients in the novel structure is the same as in the case of modified and prolonged modified Farrow structure. The novel structure offers tradeoff between filtering requirements and system delay, keeping the number of multipliers unchanged, as it is shown through examples.