考虑负频分量影响的FFT插值算法

FFT interpolation algorithm considering the effect of negative frequency component

采用加矩形窗FFT插值算法,谐波的负频分量对谐波计算的误差影响较大。为了提高结果的精确性,大多采用多项余弦窗插值的方法,这些窗的主瓣较宽,降低了计算速度和实时性。为此首先分析了泄露误差的产生,然后提出了考虑负频分量影响的矩形窗插值FFT算法。由于最少只需采样2个周期,所以该算法实时性好,采样点数少,计算速度快。为了提高运算精度,考虑了各次谐波旁瓣的影响。为了减小插值FFT算法的计算量,采用三次样条函数逼近加矩形窗的插值函数,计算量小,实时性好。仿真计算结果表明,采用该方法得到的幅值和频率都具有较高的计算精度。

For rectangular window FFT interpolation algorithm, the negative frequency components of harmonic components have a greater impact on the fundamental calculation error. To improve the accuracy, they use a number of cosine window interpolation methods, which would reduce the computing speed and real-time. First, the paper analyses the reason of the error leaked, then introduces the rectangular window FFT interpolation algorithm considering the impact of the negative frequency component. The rectangular window has narrow main flap, short sampling period and a good real-time, and using a cosine signal to the input signal is derived formula closer to the actual situation. Because only two sampling periods, using sampling points are fewer, and faster computing speeds. In order to increase computing precision, the paper takes into account all the harmonics side lobe impact, To reduce FFF interpolation algorithm computation, using cubic spline function approximation increase rectangular window interpolation function has a small amount of computation and a good real-time. Simulation results show that the amplitude and frequency have a high level of accuracy using this method.