基于三次样条函数的加Blackman-harris窗插值FFT算法

Blackman-harris window interpolated FFT algorithm based on cubic spline function

使用加Blackman-harris窗插值快速傅里叶变换(FFT)算法计算电力系统谐波时,其频率修正系数公式和复振幅的插值修正函数过于复杂。提出利用三次样条函数逼近其频率修正系数的7次多项式和复振幅的修正函数,采用三次样条插值函数的有效形式计算频率修正系数和复振幅的修正系数,将插值FFT算法的频率修正系数曲线分为10段,给定11个等间距插值点,并将复振幅修正系数曲线以频率修正系数间隔0.1分为10段,给定11个等间距插值点,分别构造出频率修正系数和复振幅修正系数的快速计算公式。公式简单,计算量小,程序实现方便,实时性好,并且在分段处连续,分段处的计算值为精确值。仿真结果表明,该算法计算所得幅值误差小于0.01%,频率误差小于0.003 Hz,相位误差小于1%。

During power system harmonic calculation with Blackman-harris window interpolated FFT（Fast Fourier Transform） algorithm, its formula of frequency modification coefficient and function of harmonic amplitude correction are too complicated. The effective form of cubic spline function is proposed to approach the seventh multinomial of frequency modification coefficient and the function of harmonic amplitude correction. Both the frequency modification coefficient curve and the harmonic amplitude modification coefficient curve are evenly divided into 10 parts with 11 interpolation points to construct the fast calculation formulas, which are simple and easy for programming, with less calculations and precise continuous values at interpolation points. Simulative results show that, it has the amplitude error less than 0. 01% , the frequency error less than 0. 003 Hz, and the phase error less than 1%.