How to get the frequency-time diagram of sound like on SoundCloud?

Question

Audio

Hello,
please tell me where to dig on the topic. Preferably, of course, an option for iOS. But, in principle, I will be glad to any solution in C / C ++.
Thank you!

Answer 1

http://www.codeproject.com/Articles/14873/Simple-Audio-Out-Oscilloscope-and-Spectrum-Analyze

Done via FFT (Fast Fourier Transform)