Signal frequency measurement by rational approximations

Analysis of jitter influence in fast frequency measurements

“…2a, and we get an assumption that most important factor able to affect our principie in [1] is a noise in a time domain, or just timing jitter. So, in our furthering simulation of the frequency measurement we will consider this special phenomenon with all related physical characters.…”

“…In other words, each pulse of the train has independent from other pulses its phase displacement with arbitrary behavior limited by corresponding distribution law. This fact we take as Relation between the jitter noise and amplitude noise (a) [3], experimental screenshots for a series of best coincidences in a presence of jitter (b and c) [1].…”

“…It gives only a possibility to find out the true phase position using a special formalism of number theory [11] introduced in [1].…”

“…This general and characteristic behavior of results is dependent of ratio between the frequencies of both pulse trains (or similarly the ratio of their periods) and their pulse widths. In computational experiments which is controlling the pulse width in each pulse train, a nonmonotone decreasing characteristic and an alternating convergence to a local míni-mum of frequency uncertainty is evident, in short measurement time (less than 1 s for given frequencies) [1].…”

“…A measure of the desired frequency can be obtained multiplying the known standard frequency by the ratio between the desired count and the standard count obtained in the two digital counters [1].…”