Weighted least-squares design of wide-band interpolation kernel

This paper proposes a frequency-domain method for optimally designing interpolation kernels that are constructed by two piecewise polynomials of second-order. Subject to a few constraints imposed on the interpolators, the optimal piecewise polynomial coefficients are found by minimizing the weighted least-squares (WLS) error between the frequency responses of ideal and actual interpolators, Through adjusting the weighting functions for different frequency bands, an accurate frequency response in a wide passband can be obtained and a don't care band can even be ignored. As a result, the proposed design approach can yield various interpolators for interpolating different discrete signals with different frequency components. Several examples are given to demonstrate that the resulting wide-band interpolator can achieve higher interpolation accuracy with reduced computational complexity than the existing interpolators.