I have an advanced question that I decided to post here in case there are some who contribute to this forum who have expertise in signal measurement. I am developing a test procedure for characterizing the stability of some hobbyiest 10 MHz oscillators. This is in preparation for a study of a couple of 10 MHz distribution amplifiers. (For the record, I intend to make the results of this study available under the creative commons attribution-share alike license and I get no financial gain from the project - I am doing it to satisfy my curiosity.) While researching background information for this project, a question arose that I have been unable to answer through Googling appropriate words and phrases.
An oscillator is mathematically characterized as:
v(t) = [V0 + e(t)] * cos[w0*t + phi(t)], where V0 is the base oscillator amplitide, w0 is the base oscillator frequency (in radians/sec), and both e(t) and phi(t) are stochasitic processes that respecitively add amplitude noise and phase noise to the oscillator's output.
For any practical oscillator, the stochastic processes e(t) and phi(t) are cyclostationary, which means their moments (e.g., mean and variance) are normally not constant (which would be true for a stationary process), but periodic. That means over time they change in value, but are periodic over some timeframe.
My problem is how to properly sample cyclostationary processes such as e(t) and phi(t). My uneducated gut feeling is that if I am attempting to characterize short term oscillator stability, I would want the time during which multiple samples are drawn (one sample being, for example, the number of zero crossings during an interval) to be defined so the moments of the probability density functions of e(t) and phi(t) vary only slightly. Otherwise, the samples at the beginning of the sampling period (i.e., the total time during which samples are drawn) would be influenced by one set of moment values and the samples drawn later would be influenced by another significantly different set of moment values.
To characterize long-term stability, my gut feeling is to use a sampling interval during which the moments of e(t) and phi(t) "cycle" several times. This would allow the calculation of an "average" of these moments.
Of course, even if my gut feelings are correct, it isn't clear how to determine an appropriate sampling period. Without getting into a lot of experimental work attempting to characterize the cyclostationary process associated with each oscillator (which is probably beyond the reach of my equipment and skill), I was hoping some general rules of thumb have been developed for common oscillators.
In addition, I was wondering what parameters might control the cyclostationary processes. The ones I could come up with after googling a bit are (with no distinction between short-term and long-term): temperature, humidity, power supply ripple, crystal and electrical component aging, mechanical vibrations, variations in loading. Some of these can be controlled in the short-term (e.g., temperature, humidity, mechanical vibrations), while others are probably only long-term factors (e.g., crystal and electrical component aging).
Given this background, my questions are: is my gut feeling about short-term and long-term sampling intervals correct, and if so, are there any general guidelines that would help me to develop an experimental design in regards to this question? Are there other parameters that would contribute to variation in the cyclostationary processes?