| Both the difficulties and solving idea of four-parameter sinusoidal curve-fit with partial period waveforms are introduced in this paper, 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-fitting 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 estimation 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. |
