A circuit which was invented ‘in the analog days’, a Correlation Cancellation Loop, has numerous uses even today. This is the basic diagram:
What this circuit attempts to do, is to provide an output, which is approximately equal to the main input, with the modification being applied, that the output should not correlate with the ‘reference input’ (in my terminology). Due to the origin of this circuit, it has a very basic way of operating. A phase-discriminator monitors the output as well as the reference input, and determines by how much they correlate.
Here, the type of discriminator which was once used had as property, to output a voltage of zero, if fed two sine-waves that were 90⁰ phase-shifted. For any other phase-shift, a non-zero output voltage resulted. A discriminator was also used for RF purposes, as part of a Frequency-Modulation Demodulator. But a CCL did not tend to be used at RF frequencies.
The output from the discriminator was then fed into an integrator, where practical integrators are actually first-order low-pass filters. Electrical Engineers don’t really want the output-gain to go to infinity, just because the input-frequency was low, or because the input was consistently non-zero. And so below some frequency, the response-curve of practical integrators levels off. But for conceptual purposes, they are operated as integrators, somewhere along their -6db /Octave falloff curve.
The intent is, for the non-zero correlation of the output to modulate the reference signal – positively or negatively – such that the modulated result gets added to the main input, eventually to result in a correlation of zero. Hence, it was assumed that the two inputs had some amount of correlation to begin with, so that some product of the reference input could either be added to or subtracted from the main input, to achieve a hypothetical absence of the signal at the reference input, from the output.
(Updated 07/18/2018, 20h35 … )