A Fractional Spur Cancellation Technique for Fractional-N Frequency Synthesizers Enabled by Dual Loop Phase Clamping

Yan, Tanwei; Jiang, Junning; Silva-Martinez, Jose

doi:10.1109/TCSI.2025.3557837

An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values of

α < 1

lead to an increase of short time intervals, but occasionally allow for very long time intervals. When

α = 1

, the f-coalescent and the Kingman’s n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that n genes descend from m ancestral genes in a time interval of length T for the f-coalescent are derived. The f-coalescent has been implemented in the population genetic model inference software Migrate. Simulation studies suggest that it is possible to accurately estimate α values from data that were generated with known α values and that the f-coalescent can detect potential environmental heterogeneity within a population. Bayes factor comparisons of simulated data with

α < 1

and real data (H1N1 influenza and malaria parasites) showed an improved model fit of the f-coalescent over the n-coalescent. The development of the f-coalescent and its inclusion into the inference program Migratefacilitates testing for deviations from the n-coalescent.

More Like this