That's going to be rather hard.
As rule, crap in, crap out.
And it applies to radio as well: if the signal you are getting is weak and/or you are getting allot of noise, then there is not allot you can do. And if your squelch is having trouble filtering signal from non-signal, I am willing to hazard a guess that you have a rather lot of noise.
The first thing I would recommend is to increase the amount of signal coming into whatever antenna your radio is using, the stronger the signal, the better the signal to noise ratio is, and the more you can do. Next, try to eliminate unnecessary sources of noise around the radio, things like microwaves and unshielded computer components. Again, your goal is to increase the Signal to noise ratio as much as possible before you attempt to process the signal.
If you insist on actual signal processing, I can tell you the basics of what needs to be done. You probably want to start by applying pass filters to take out as much periodic noise as possible, but that should be mostly taken care of by the radio itself. Next you can take the signal, amplify it significantly, then just increase the noise floor cutoff to compensate. You loose allot of the signal doing this, and if your S/N ratio is bad, you probably won't retain much of the original signal, but it can work for limited amounts of noise.
I am an electronics student (and not a radio expert at that). So I am approaching this from a hardware filter standpoint, but that still might be your best approach. Simple noise reduction programs can be rather
costly. And I don’t know if any of them can do real time DSP. There is apparently a half decent free audio program called
WavePad, but I have no clue if it can do the on the fly stuff you are looking for.
Your best bet is talking to an actual radio expert, they can tell you most of what you are looking for, if it can even be done.
Finally, how do we know you are not a terrorist in disguise? You sound rather suspicious to me… :p
"Well, if I am not drunk, I am mad, but I trust I can behave like a gentleman in either
condition."... G. K. Chesterton
“questions are a burden to others; answers a prison for oneself”