Prolonged transposed polynomial-based filters for decimation

If sample rate conversion (SRC) is performed between arbitrary sample 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. The impulse response of these filters is of a finite duration and piecewise polynomial so that it is expressible in each subinterval of the same length T by means of a polynomial of a low order. Here, T can be equal to, a multiple of, or a fraction of either the input or output sample period. The actual implementation of the polynomial-based filters can be performed directly in the digital domain effectively by using the Farrow structure or its modifications. This paper introduces for an arbitrary sampling rate reduction a novel implementation form referred to as the prolonged transposed modified Farrow structure. For this structure, T is an integer multiple of the output sampling period. Compared with the modified transposed Farrow structure, it has a narrowed pass-band region with almost the same complexity. In addition, a decimator structure consisting of a cascade of the prolonged transposed Farrow structure and a fixed linear-phase finite-impulse response decimator is introduced in order to reduce the overall computational complexity.