残周期正弦波形参数拟合及其应用

Curve-fit Method and Its Application of Four-parameter Sine Wave with Partial Period

介绍了残周期正弦波拟合问题的难点及解决思想:以无需初始值预估计的模型拟合方式,化解残周期波形时信息不够全面的问题,从而一举解决了残周期条件下的正弦波形最小二乘拟合问题。针对残周期条件下的正弦拟合的特殊性,介绍了正弦波局域失真的思想及概念,以及适应于局域波形的噪声信号比的概念,并给出了噪声信号比对于正弦参数拟合误差的影响规律。针对残周期正弦波拟合的应用,给出了几个典型的应用事例,包括超低频正弦参数的快速估计、AM和FM信号波形的数字化解调、冲击波形峰值的精确估计、其它正弦波拟合算法的初始值估计等。证明了方法的有效性、可行性和工程实用价值。

Both the difficulties and solving idea of four-parameter sinusoidal curve-fit with partial period waveforms are introduced in this pa-per, and through the method without pre-estimation of initial value of four-parameter, the problem of less information of partial period is solved. So the pre-estimation of four-parameter in sine wave curve-fitting is not needed. Aiming at the specialty of four-parameter curve-fit with partial period, a definition about the local distortion of sinusoidal waveforms is presented, and the definition of Signal to Noise Ratio of sampling series（ SNR） and the Noise to Signal Ratio of sampling series（ NSR） are put forward. By using the method of varying known parameters of partial period of sinusoidal waveforms and the Gauss noise level, when the width of period, phase, and SNR are varied, the varying rules of curve-fit-ting error of partial period sinusoidal are studied by experiments. The results show that, in partial period sinusoidal curve-fitting, the varying rule between NSR and phase of sinusoidal series is fixed, and all the curve-fitting errors of amplitude, frequency, phase, and DC bias vary as NSR. The partial period sinusoidal curve-fitting errors can be estimated by using simulation with curve-fitting parameters. In some experiments, including the fast parameter estimation of ultra-low frequency sine wave, the demodulation of AM, FM and PM waveforms, and the precise esti-mation of peak of impulse, and the initial value estimation of other sinusoidal wave forms curve-fitting, the validity and feasibility of the method are proved.