[VLM]

Only kind of. If someone hasn't seen fit to write the code for a 240 hz morse code filter, you don't get one. Or a very advanced AGC filter. Those are "easy" because you could modify an existing set of code, assuming open source application. GNUradio has a compile/run architecture although you can build rather highly configurable real time systems so it's "close" to programming in real time.

Harder is something like "digital radio monodiale" which aside from having an unfortunate acronym is a digital shortwave voice modulation scheme... without having the specs in front it would be very hard to decide where to start. There are military intelligence people who do exactly this stuff with captured enemy signals, given an enormous head start of knowing the rough technology level of the other side and maybe some stolen documents. Still its not easy for them. A good analogy would be imagine a radio intelligence officer in WWII heard some 8VSB over the air broadcast TV from 2015... honestly I think you'd end up with question marks for at least 50 years trying to figure that signal out in 1940.

Right now, perhaps we are getting a 40 dB below the noise digital data signal from space aliens. Without any idea how to build the specific demod, we're going to get nowhere, and a level that low below the noise floor will not show up on any normal waterfall so we'd likely miss it.

Existing modes tend to reflect hardware ability. So some gear some of the time is stable enough to use WSPR modulation which is an ultra low bandwidth digital mode for HF (shortwave)... some gear drifts in frequency too much to use it, today. Oscillator stability can be improved to make it work, but replacing the IF stages with A/D converters won't do it, takes more than just doing demodulation in software with SDR instead of in hardware to fix the root frequency stability problem. Its possible space aliens modulation method would assume close in phase noise or IMD performance beyond 2015 capabilities, because for them its trivial star trek dilithium crystal stuff or whatever, but we're not going to invent the noise free monochromatic oscillator for another 150 years or whatever, so the front end performance of our radios wouldn't be good enough even with a preprogrammed SDR on the back end to demodulate. Another example, we don't have the technology today or the legal framework to do "real" beyond ultra wide band RF work, but there's no reason to think space aliens wouldn't.