Efficient Implementation of Cubic Spline Interpolator

Abstract

In this paper, we present a novel implementation of cubic spline interpolation (CSI). In addition to solving the time domain boundary conditions between neighboring samples, we optimize the coefficients of piecewise polynomials in frequency domain to achieve good in-band and out-of-band frequency responses while maintaining the low-latency and low-complexity properties of a conventional CSI. To demonstrate the advantage, a 200 MHz instantaneous bandwidth (iBW) signal consisted of two 100 MHz 5G New Radio (NR) waveforms is adopted in simulation. The results show that the proposed CSI can achieve a normalized mean square error (NMSE) of -65.6 dB compared to -37.1 dB obtained with the conventional CSI. The proposed method is not penalized by the aliasing effects due to Nyquist sampling, as the ratio of sampling rate to signal bandwidth approaches 2.5x.