基于分段多项式拟合的数字信号插值方法

Digital Signal Interpolation Method Based on Piecewise Polynomial Fitting

传统的数字信号插值方法多采用固定系数多项式,导致系统性能提升空间受限。针对该问题,提出了一种系数优化的分段多项式插值方法,利用具有边界条件的最小二乘法对一个预先设计的插值滤波器冲激响应进行分段拟合,从而对插值多项式进行系数优化。该方法可有效控制插值结果与真实信号波形间误差,提高信号插值精度。仿真结果表明,该方法可有效提升插值器性能,降低插值带来的信噪比损失,可用于提升数字通信系统符号同步、重采样或采样率变换的性能。

The polynomial with fixed coefficients is often adopted in the traditional digital signal interpolation method,and it causes the limited performance increase space.Aimed at the problem,apiecewise polynomial interpolation method with optimized coefficients is proposed.The least squares（LS）method with boundary conditions is utilized to carry out the piecewise fitting against the impulse response of a pre-designed interpolation filter.Thus,the coefficients of the interpolation polynomial are optimized.With the method,the error between the interpolation result and the actual signal waveform can be controlled,and the interpolation precision of the signal is improved.Simulation result shows that the method can increase the interpolation performance,and it can debase the SNR loss caused by the interpolation.The method can used to increase the performance of the symbol synchronization,the resampling or the sampling frequency conversion in the digital communication systems.