Formula to invert sound?

Question

Currently, I'm trying to make an app that cancels out sound. I have everything setup, it can analyze what frequency is coming in from the microphone and it can play any frequency. Although, now I am stuck because I am trying to find a good algorithm. Could someone help me find an algorithm, and possibly explain the math involved in it because I'm in high school and have not taken physics yet. I have researched sound cancellation and get the main concept of it. I am working in Xcode using Swift, just to inform you.

Answer 1

You can check out Wiener Filtering from Wikipedia. Using a wiener filter, you can estimate the background noise up to a few samples. Then subtracting these estimated noise samples from the audio you may suppress the noise.