Study On The Method Of Precise Determination Of A Periodic Signal

It is important for us to determine the period, amplitude or phase of a periodic signal. We can use the method to solve many problems. For example, we can use it to determine the period of a torsion pendulum in measurement of Gravitational Constant G by the means of the swing time method, and we can use it to determinate the amplitude of signal with known frequency in detection photon rest mass. I have done some work on precise determination of the period or amplitude of a periodic signal as follows:1, I have read many papers on determination of period of a periodic signal. These methods will be discussed in my paper.2, I have read many papers on noises, and low frequency noise 1/f will be briefly summarized.3, High precision value of G could be measured by means of the swing time method of the torsion pendulum, where the precision of G is mainly dependent on the precise of the period of a torsion pendulum. In order to improve the precision of G, the period of a torsion pendulum should be measured with precision as high as possible from the experimental data. However, it is very difficult to acquire a precise measurement of the period of a torsion pendulum because the motion of the torsion pendulum is strongly influenced by various external disturbances. We have studied the character of the motion of the torsion pendulum, and discussed how torsion pendulum responds to external shock and how the period of the torsion pendulum is changed. We have settled down the trouble problem which is precise determination of period of a torsion pendulum by correlation method. Theoretical analysis agrees well with the result of the experimental data processing.Detection of the photon rest mass is dependent on a rotating torsion pendulum method, where the precision of the experimental result is mainly dependent on the amplitude of the modulating signal. In order to precise determination of the amplitude of a single with a known frequency, we establish a Gauss color noise model. Based on Gauss color noise model, the root-mean-square deviation of the amplitude for a sinusoidal signal with known frequency in each period is deduced, and then the correlation analysis and the weighting statistical analysis are incorporated to improve the precision of determining the amplitude of signal. The uncertainty of determining the amplitude has been improved about four folds than before in dealing with the experimental data which is determining limits on the photon mass.