About sum of signals and possible use in time and frequency systems

The author analyzes the frequency of the sum of sinusoidal signals. It is shown that if the signals are roughly phase aligned then the frequency of the sum is a weighted average of the frequencies of the signals and the fractional frequency noise is reduced in the summation. The Allan deviation of a signal whose phase is modulated by various wave shapes is analytically and numerically calculated. These include sine-wave,, sawtooth-wave, and a general periodic function modulation. The calculations are used to analyze the stability of a sum of signals in various cases. A possible use of signals addition in time and frequency generating systems in which several frequency sources are used for redundancy is discussed. One can make optimal use of the frequency sources by simply adding the signals with predetermined amplitudes (weights) to achieve a better short-term stability and a redundancy at the same time