Polynomial-based filters with odd number of polynomial segments for interpolation

In many signal processing applications, it is beneficial to use polynomial-based interpolation filters. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. In the literature only polynomial-based filters having even number of polynomial pieces N have been considered. This letter presents a modification of the implementation form which allows realizing polynomial-based filters having an odd number of polynomial pieces. The condition that N must be even integer is not required any more. Further, a frequency-domain filter optimization method is developed, based on the methods for even-length filters. We illustrate through examples the performance of the odd-length polynomial-based filters.