Besides some very basic circuits (voltage divider, full-wave rectifier with 4 diodes) and a little bit of Arduino programming I am completely new to electronics. Can you please give me a couple of phrases that I could use on Google to point me into the right direction?
Sure--
https://www.google.com/search?&q=white+noise+circuit&oq=white+noise+circuit (the one on EDN is pretty standard, and will work -- arguably, too simple for even EDN to screw it up!
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https://www.google.com/search?q=2nd+order+low+pass+filter+calculator (the Okawa-Denshi calculators are reasonable; mind: if you put in UNreasonable component values, you will get unreasonable values out! It's a calculator, not a designer. Sanity is your responsibility.
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A Sallen-Key or MFB topology, with Butterworth characteristic, is an absolutely standard way to go, and gives good results. (You can use the other half of that LF412, instead of using the x100 output in the EDN circuit.)
Tight filtering can be harder. The general approach is to make a nearly unstable amplifier, by putting resistors and capacitors into the feedback loop. Or to put it another way, making a modest quality LC resonator, by faking the inductor with an op-amp and capacitor (op-amps can be used to convert and invert impedances!). You'll see this for bandpass or "frequency boost" types of circuits.
(Oops, dropping more terminology; give "LC resonant tank circuit" a look. Basically, the electronic equivalent of a mass and spring.)
Another approach is to set up an oscillator, and control its frequency based on some comparison with the input signal (which in this case, would be the white noise). When the comparison is done with a phase detector or RF mixer, the result is called a PLL (phase locked loop).
A PLL can be expressed as a kind of bandpass amplifier, though usually with much better performance than you'd get from trying to make a brute-force filter. They're also much quirkier (lock/unlock behavior, nonlinearity), and can be more useful (the frequency control voltage has useful properties, like tracking frequency modulation -- intuitively, a PLL following an FM signal must have the original signal controlling its own oscillator, right?).
https://www.google.com/search?q=tone+detectorThe old LM567 (and relations) is a classic. It's an analog circuit, so is well suited to this sort of thing. There should be example circuits that show this sort of function (narrow bandpass filtering).
(There are other kinds of "locked loops" besides PLLs. Other detectors can be used, to get FLLs (frequency), DLLs (delay) and so on. The "locking" generally refers to controlling one parameter (e.g., frequency, or say, mechanical servo velocity) based on a physical relation to the detected signal (phase, position), thus locking the parameter *exactly* in place, with no error).
Once you have your filtered signals, you can "OR" them together using an audio mixer. The most basic version of this is, you take the output voltages from each block, wire them together with series resistors, and amplify. Often, the amplifier is an inverting type, so all the resistors meet at a "virtual ground" (the op-amp holds -in = +in thanks to feedback), which prevents the signals from seeing cross-talk (more important in something like an audio mixing board than here, but an important lesson).
Tim