Analyzing the Probability of Overlap between Two Periodic Pulse Signals during an Arbitrary Observation Time

Analysis of overlap in the time domain is the fundamental of research on the interaction between two periodic pulse or events. However, the study on the characteristics of overlap during an arbitrary observation time has not been presented. Therefore, this paper attempts to build an analytical model for calculating the average probability of overlap (APO) based on the joint probability distribution function. The starting time and serial number of the pulse are considered as two random variables. Accordingly, the difference between two edges of the pulse is a function of starting time and serial number, thus cumulative distribution function (CDF) of the difference between two edges of the pulse can be derived. Results of this paper show that the APO of every pulse in an arbitrary time equals the ratio of the sum of pulse duration of two pulses to the periodicity of overlapping pulse except the first pulse. To conclude, this study may be of importance in analyzing electronic interference between two equipment, as well as in providing a method on anti-jamming.