I'm not saying every analog signal processor is surely memory free, simply that you can imagine one that is.

But I'm not really familiar with what that is.

They're a kind of analogue dynamic memory. I'd hesitate to call them RAM because the Access is not Random, but they are a kind of shift register and early computers used those for RAM.

Imagine a pair of MOSFETs connected to a pair of capacitors, and a bunch of those joined together in a chain. All the gates of each one of the pair of MOSFETS are connected together, giving you a "left" and "right" clock input.

When you put a signal in if you pulse the "left" and "right" inputs, it'll store the signal voltage in one capacitor, then pass it off to the next capacitor in turn, like old-timey firefighter handing buckets of water down a line of people.

They used to use this for delaying audio signals before digital memory and analogue to digital conversion was cheap enough to use.

	▲	fsckboy a day ago \| parent [-]
		bucket brigades were also used to read large scale sensors like a CCD camera. they are more efficient in their use of die space because you need fewer data paths; they don't need to be digital either, each bucket can be analog for "grey" scale