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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?

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

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  • $\begingroup$ So then where does the sin come in? $\endgroup$ – user782220 Jul 27 '12 at 9:20

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