Polynomial-based Filters in Bandpass Interpolation and Sampling Rate Conversion

If the 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 with the impulse response ha(t) having the following properties. ha(t) is nonzero for an interval 0 ≤ t < NT with N being an even integer and is expressible in each subinterval of length T by means of a polynomial of a low order. The length of polynomial segments T can be equal to the input or output sampling interval, a fraction of the input or output sampling interval, or an integer multiple of the input or output sampling interval. The advantage of mimicking the above system lies in the fact the actual implementations can be performed effectively by using the Farrow structure or its modifications. So far, the polynomial-based filters have been used only for baseband interpolation and SRC. In the literature, it has been observed that in the passband applications the filter order of the polynomial-based filter increases. In this paper, we study application of the polynomial-based filters for the bandpass interpolation and SRC. It is shown that the polynomial-based filters, implemented using Farrow structure or its modification, can be effectively used also in the bandpass applications. We show through examples that the filter order is the same as for the corresponding baseband filter having same requirements.