In the documentation for the [XAudio2 filter parameters] it mentions

Filter radian frequency calculated as (2*sin(pi*(desired filter cutoff frequency)/sampleRate))


Where does this formual come from? What is "Filter radian frequency" and "filter cutoff frequency" and what is the difference. Can someone translate this terminology to mathematics of DFT?

• Duplicate (same user on Stack Overflow): XAudio2 filter radian frequency - question has been satisfactorily answered there so this dupe should probably be deleted ? – Paul R Jul 24 '12 at 22:09
• Can you post a link to the documentation where you found this line? – Phonon Jul 30 '12 at 17:11

That is simply converting analog frequency into digital frequency. For example, if you want a cutoff of 1kHz at a sample rate of 44.1kHz, the corresponding digital frequency is 2*pi*1000/44100 = 0.142... radiants. In terms of DFT the digital frequency is the $\omega$ in the $e^{^-j\cdot \omega }$ term of the DFT