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I'd like to do a fade out of a sound in a few seconds, but in a "spectral way", with a special curve : enter image description here

(here x-axis is time, y-axis is frequency from a few hz to 20khz).

All the part "to be removed" has to be removed !

Do you know how to do this ? (an EQ / simple IIR/FIR filter won't work for this, etc.)

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You want a time-varying low pass filter, automated so that the cutoff frequency follows your curve. For such slow modulations most IIR low pass filters are stable, so you can just find a steep enough low pass filter and update its coefficients while filtering while keeping the filter state.

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    $\begingroup$ One simple option might be a leaky integrator. This is a first-order lowpass IIR filter that only has one parameter, $\alpha \in (0,1]$. You can sweep the parameter across a range of values as needed to adjust the cutoff frequency. $\endgroup$ – Jason R Nov 14 '13 at 12:58
  • $\begingroup$ A two pole filter is likely to give a more musically interesting response (as this is a slope found in many synthesizer filters). Something as simple as the Chamberlain state-variable filter will do. $\endgroup$ – pichenettes Nov 14 '13 at 15:48
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In the same way that an low pass filter can cutoff frequency following your curve, an EQ too can be used with the same idea of time-varying

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