The magic constants come from the unofficial "ITU-R BS.1770-1 filter
specifications"¹ by Raiden (libebur128) which relies on "Parameter
Quantization in Direct-Form Recursive Audio Filters"² by Brian
Neunaber.
The constants seem to include a quantization bias, for example:
- Vb is supposed to be exactly √Vh in a high shelf filter
- the Pre-filter Gain should likely be 4dB
- Pre Q and RLB Q are respectively very close to √½ and ½
Those are not adjusted to prevent the values from drifting away from
the official specifications.
An alternative to this approach would be to requantize on the fly as
proposed by pbelkner³, where the 48kHz code path would use the exact
specifications constants while derivating constants for other
frequencies.
[1]: https://www.scribd.com/document/49991813/ITU-R-BS-1770-1-filters
[2]: https://www.scribd.com/document/6531763/Direct-Form-Filter-Parameter-Quantization
[3]: https://hydrogenaud.io/index.php?topic=86116.msg740092#msg740092
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