A poly-phase based interpolation filter computation involves an input-matrix and coefficient-matrix of size (P×M) each, where P is the up-sampling factor and M=N/P, N is the filter length. The input-matrix and the coefficient-matrix resizes when P changes. An analysis of interpolation filter computation for different up-sampling factors is made in this paper to identify redundant computations and removed those by reusing partial results. Reuse of partial results eliminates the necessity of matrix resizing in interpolation filter computation. A novel block-formulation is presented to share the partial results for parallel computation of filter outputs of different up-sampling factors. Using the proposed block formulation, a parallel multiplier-based reconfigurable architecture is derived for interpolation filter. The most remarkable aspect of the proposed architecture is that, it does not require reconfiguration to compute filter outputs of an interpolation filter for different up-sampling factor. The proposed structure has regular data-flow and it has no overhead complexity for its reconfigurable feature unlike the existing structures. Besides, the proposed structure has significantly less register complexity than the existing structure and its register complexity is independent of the block-size. Moreover, the proposed structure can support higher input-sampling frequency than the existing structure. ASIC synthesis result shows that the proposed structure for block-size 4, filter length 32, and up-sampling factor 8, involves 13.6 times more area and offers 245 times higher maximum input-sampling frequency compared with the existing multiplier-less structure. It involves 18.6 times less area-delay-product (ADP) and 9.5 times less energy per output (EPO) than the existing multiplier-less structure.