All algorithms for noise reduction are at least as complicated as the pretty simple low-pass, and many would be more complicated. So, the solution is this: stop scaring yourself by "little complicated" and get to work. Don't trouble trouble until trouble troubles you :-)
[EDIT]
If you need to find some available codes, I would advise to look at the source code of open-source Audacity software:
http://audacity.sourceforge.net/[
^].
If has the pluggable tools for editing of the audio, including noise removal. You can find out and get its source code to see how it works:
http://wiki.audacityteam.org/wiki/Noise_Removal[
^].
See also:
http://en.wikipedia.org/wiki/Noise_reduction[
^].
—SA