I have a mathematically sound suggestion but I do not know how well it will work in application. Most period measurements measure the time between a full period or several periods to eliminate the error introduced by the measuring device. Essentially the device error is made insignificant.
Mathematically you can do much more but there is a tradeoff between recording less information and knowing (or assuming) some values. For instance, if one knew the amplitude and could calculate the derivative of the signal, one could calculate the frequency. A sine wave can be represented by the function: A sin (BX)=C , where A is the amplitude, B is the frequency, C is the present measured value. If the equation is solved for X, we get: X=(sin^(-1)(C/A))/B. The d
erivative of the first equation is AB cos(BX)=C. If the equation for X is now substituted into the second equation, we get, AB cos(B (sin^(-1)(C/A))/B)=C. Solving for B we get B=C/(A cos(sin^(-1)(C/A))). Remember, we already know A and C, so we are done.
Practically every step and assumption in the above argument introduces possible error which will affect the accuracy of the frequency. Unfortunately it is a trade off and that is why at least a whole period needs to be measured to get an accurate frequency.
Jeremy Braden
National Instruments
