I would like to build "radio ears", a RF receiver that would allow me to experience the RF "smog" around us as sound in my headphones. A more sophisticated version of the cellphone-to-speakers interference we all know. I'd like to walk through buildings and streets and find out which places are "quiet" and which are "loud". Or to hear that a new WiFi transmitter has been installed upstairs. Also, to hear what sources have higher carrier frequency and which ones have lower. And hear the silence when there is a blackout. Some people call this "augmented reality".
A simple crystal radio without tuning would receive all carriers (rectification only), but I would like the circuit to somehow preserve information about the carrier frequency. For example, if it were the year 1910 and the air would be full of wireless telegraph transmissions, I would like to hear them beeping one over the other in my headphones, with the frequency of the acoustic sinewaves scaling with the frequency of the telegraph transmitter's RF carrier (e.g., 1 MHz transmitter -> 1 kHz in headphones, 1.5 MHz -> 1.5 kHz).
Technically, I want to scale the frequencies, not shift them, and that is where the problem lies!
Is such a circuit possible at all? Mathematically, I want to squeeze a 1000 times larger bandwidth into a smaller one, so there has to happen some information loss. However, I was not able to come up with a reasonable mathematical description of what kind of loss this should be (its none of the simple things like low-pass, band-pass, frequency shift etc.).
Right now, I'm not looking for performance, but rather for the principle. The question is: what kind of simple analog circuit would turn 1 MHz into 1 kHz and 1.5 MHz into 1.5 kHz?
edit: if you suggest a digital algorithm or a mathematical formulation, I'd like to stress that I need it to be (almost) real-time. To produce 1 s of output from each 1 s of input. In other words, to be able to listen to several 1910's telegraphers transmitting Morse code at the same time (and write it down with my eight hands :) )