应用三次样条函数快速计算插值FFT算法

Fast calculation of interpolated FFT algorithm using cubic spline function

加汉宁窗插值快速傅里叶变换(FFT)算法可以克服频谱泄漏的影响,消除用异步采样值测量电量时产生的误差,但其计算量较大,实时性较差。为了减小插值FFT算法的计算量,采用三次样条函数逼近加汉宁窗插值FFT算法函数,提出了应用三次样条函数的有效形式计算插值FFT算法,将插值FFT算法的谐波幅值修正系数曲线分为10段,给定11个等间距插值点,构造出计算插值FFT算法的三次样条函数的快速计算公式。该公式简单,程序实现方便,计算量小,在分段处连续,且为精确值,可以大幅度提高插值FFT算法的计算速度和实时性。仿真计算结果表明,应用三次样条函数的有效形式计算电量谐波幅值和频率,幅值误差小于0.1%,频率误差小于0.01Hz。

Hanning window interpolated FFT（Fast Fourier Transform）algorithm can overcome the influence of frequency spectrum leakage and eliminate the errors brought by using asynchronous sampling values in electrical parameter measurement, but it needs a large number of computations and has bad real-time performance. In order to reduce its computations, the cubic spline function is adopted to approach Hanning window interpolated FFT algorithm function,the effective form of cubic spline function is put forward to calculate the interpolated FFT algorithm. The harmonic amplitude modification coefficient curve is divided into 10 parts and 11 interpolation points with equal intervals are given to form the fast calculation formula using cubic spline function for Hanning window interpolated FFT algorithm. It is simple and easy to be programmed with less calculations and precise continuous values at interpolation points,and the speed of interpolated FFT algorithm is improved strongly. Simulative calculation results show that,the power harmonic amplitude and frequency calculation using the effective form of cubic spline function has the amplitude error less than 0.1% and the frequency error less than 0.01 Hz.