C++ audio library to edit audio files/live audio

[new hope]

I need someone who has links to a good C++ audio library that allows you to edit audio files or live streaming audio from a computer mic. This edited audio needs to be able to recorded and saved to file or sent via winsock or accessed via other C++ libraries whether it is via file or via real live stream directly from computer mic.

I found a couple of libraries but they just allowed you to play audio files and pause them ect. I need to be able to actually edit live audio from computer mic and saved audio files. I need a library with advanced audio editing features. Not just splicing audio but the ability to perform mathematical operations on the frequency and wavelengths and other properties of the audio.

Does anybody know of any good libraries for free or low cost libraries (under 100$)