Common Multiple Period Research Articles

Quasi-Synchronization for Periodic Neural Networks With Asynchronous Target and Constrained Information

This paper investigates the problem of quasi-synchronization (QS) for the periodic neural networks (NNs). In order to address more general NNs, the parameter and the period mismatches are both considered, that is, excluding parameters, periods of the target dynamic and the followers are also different. In addition, the constrainted target information is studied, where the logarithmic quantizer is used to overcome the limited communication capacity and Bernoulli processes are employed to model cases of the information loss. A new period is established based on the lowest common multiple period of the target dynamic and the followers to obtain an augmented synchronization error system (ASES). Further, a suboptimal iterative algorithm is proposed to cut down the QS range of the ASES and the corresponding controllers are designed. At last, the controller design method is illustrated by a numerical example.

Direct digitalized phase comparison between signals with different nominal frequencies

In this paper, the direct digitalized phase comparison which has phase continuous and high resolution is proposed to measure the phase variation of the high-precision frequency standard with different nominal frequencies. During the least common multiple period, the phase difference between the two comparison signals is regular, therefore the phase comparison between arbitrary frequency signals is achieved directly through using a high-speed analog-to-digital converter as the counter and the equivalent phase-detecter. By experiments and analysis, it was shown that no-interval frequency measurement can be converted into the phase difference measurement and the frequency stability evaluated as the Allan deviation accords with the change law of 1/τ.

High-precision frequency measurement system based on different frequency quantization phase comparison

Aiming at the requirements of phase comparison without frequency normalization, a high-precision frequency measurement system is proposed based on different frequency quantization phase comparison. Using group phase difference pulse in the least common multiple period, the period of frequency standard signal, the period of the measured signal and the pulse width of group phase difference can be respectively counted with the aid of FPGA technology. The obtained counter value is saved and sent to host computer. The measured frequency can be obtained by the data processing of the host computer. Experimental results show that the short-term frequency stability of the system better than E−12/s is achieved. Compared to the traditional frequency measurement system, the system have the advantages of wide measurement range, high frequency stability, low phase noise and low development cost. The system not only plays an important role in precise measurement physics fields such as high-precision transmission and comparison of time and frequency, measurement and suppression of phase noise, but also has a wider application in localization of spatial motion radiation source, satellite navigation equipment, precise time frequency measurement, communication, radar and other high-tech fields.

Precise frequency linking method based on phase group synchronization

In the precise measurement, control and processing of phase and frequency, the measurement resolution better than picosecond (ps) has an important significance on the improvement of the frequency standard technique, the precise time and frequency measurement, the time or phase synchronization processing, phase noise measurement with a wide range and quick response time and the time and frequency synchronization of bistatic radar. Aiming at the complex frequency transformation, the low measurement resolution and the uncertain frequency linking precision in the traditional frequency linking method, a new frequency linking method is proposed based on phase group synchronization. We characterize the least common multiple period between any frequencies signals, utilize the quantization step law of phase difference, establish the phase group synchronization between two different frequencies signals, transfer the frequency stability and accuracy from one signal to another, and thereby achieve the precise frequency control among any signals. It is shown by the experimental results that the frequency stability with 10−12 in 1s can be easily obtained in the quantum frequency standard, as well as the complex and precise frequency linking. Compared to the traditional frequency linking method based on frequency processing, the method has the advantage of the simple frequency chain, the low cost and the high frequency linking precision.

Research and application of regular phenomenon between periodic signals

The phase change between periodic signals is regular. Research on the regular phenomenon between periodic signals is helpful to improve the precision of some measurements and develop some new measurement methods. So it is necessary to analyze the characteristics of the greatest common factor frequency and the least common multiple period universally existing in periodic signals. The regulation of the quantitative phase shift resolution between periodic signals is presented. The cause of difference in phase characteristics between periodic signals is explained well. In this paper we propose different application prospects based on the regular phenomenon between periodic signals, with focusing on the methods for high precision frequency measurement and transient stability measurement. The experimental results are satisfactory.

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed, which is based on proposing the new concepts of the greatest common factor frequency, the least common multiple period, quantized phase shift resolution, equivalent phase comparison frequency and so on. Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail. Using the basic principle and the variation law of group phase difference, the frequency stability better than 10−14/s can be easily obtained in the time & frequency measurement and control domain, and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization, and locked precision with 10−13/s can be reached based on phase group synchronization. The phase group synchronization can provide technical support to frequency linking among radio frequency, microwave and light frequency.

On Group Phase Quantization and Its Physical Characteristics

The physical characteristics of phase quantum are further revealed, based on the proposition of concepts of the greatest common factor frequency, the least common multiple period, quantized phase shift resolution and equivalent phase comparison frequency. Then the problem of phase comparison between different frequency signals is certified in detail. Using the basic principle of phase comparison between different frequencies and the variation law of group phase difference, a point of view on group phase quantization is presented. Group phase quantum is not only an indivisible individual of group phase, but also a basic unit composing group phase difference. It is equal to the equivalent phase comparison period of phase comparison between different frequencies in size. Experimental results show not only a high measurement resolution of 10−12/s in frequency measurement based on group phase quantum, but also a super-high locked phase precision of 10−13/s in active H atomic clock.