Simple derivation and closed-form frequency-domain design of wideband length-8 interpolation kernel

This paper proposes a frequency-domain method for designing a wide-band length-8 interpolator in the weighted-least-squares (WLS) sense. The length-8 interpolator is even-symmetric and it consists of the fourth-order piecewise polynomials. In this paper, we first present a simple method for deriving its closed-form frequency response, and then formulate a frequency-domain WLS design with the C0-continuity constraint. Since the length-8 interpolator contains a total of 20 parameters, and the C0-continuity imposes 8 constraints on the design, the remaining 12 parameters can be taken as free parameters. After expressing the frequency response as the function of the 12 free parameters, the optimal free parameters can be found in the frequency-domain by minimizing the weighted squared error between the ideal and actual frequency responses, where a non-negative weighting function is adopted for emphasizing important frequency bands and ignoring unimportant bands. Consequently, the WLS design can yield an extremely accurate wide-band length-8 interpolator. Three interpolation examples are given to verify that the designed length-8 wide-band interpolator can achieve the highest accuracy in both the frequency-domain and time-domain as compared to other existing interpolators.