材料期刊网

把样条内插信号Fourier变换原理首次引入电化学界面阻抗测量,取得满意的结果。该方法完全消除了非带限信号的离散Fourier变换(DFT)中固有的混迭效应和周期化影响。不受采样定理限制,使得谱函数完全复盖整个频率轴。模拟计算表明,其精确度大大高于DFT及Laplace变换中使用的“线性近似”、“指数十线性近似”。公式推导还可以证明:在等间隔采样时,“线性近似”Laplace变换是m阶样条内插变换中m=1的特例。

In thes paper cubic spline interpolation of equidistant samples is employed for the numerical execution of Fourier transform to perform the transformation from the time domain into the frequency domain, and interracial impedance of electrochemical system can be determined. The interpolation procedure is performed implicitly by weighting discrete Fourier transform(DFT) coefficients with A_3(ω) as follows (?)(ω)=A_3(ω)·(?)(ω)+B_0(ω) (?)(ω) being DFT and B_0(ω) additive terms. In this way the aliasing effect of DFT spectrum and limitation by sampling theorem can be eliminated. So (?)(ω) is nonperiodical as being the Fourier transform of a continuous function, and the frequency range of (?)(ω) is not limited. The approximation error of numerical Fourier transform is only produced by that cubic spline interpolation. So it is one of the most accurate methods to measure the "ac impedance" in time domain at present. As it is proved in another paper, the linear approximation by Laplace transform in literature is only the case of m=1 for the m-th order spline interpolation via DFT.