[NiHaoMike]

Maybe I should just say "good quality input filters"? Granted, doing it in analog does require a lot of precision components, making it a poor choice for portable instruments where space is at a premium and where the temperature can vary widely. Doing the bulk of it in digital simplifies the analog filter requirement to to a simple antialiasing filter, with the remaining orders done in the digital domain.

Try building a purely analog circuit to measure the average power draw of a load that cycles or otherwise varies over a few hours. Don't be surprised if leakage currents frustrate your efforts. The simplest way I can think of (sticking to analog) is to advance a mechanical counter, as in an analog watt hour meter, then keep track of the time with a mechanical clock.