Relief EQ is a EQ for everyday tasks, anywhere from mixing a track to master bus.
Runs in double precision 64-bit internal processing. Also double precision input / output if supported. At 44.1 kHz and 48 kHz sampling rates, it upsamples to 88.2 kHz or 96 kHz respectively to do all EQ processing with 17 sample latency.
It starts from cramping.
Nyquist Theorem lets every DSP possible, however, it cramps infinite frequency into limited range.
It causes frequency and phase response of an EQ to be mismatched from analog, or theoretically perfect response.
In result, high bells will be narrower and looese symmetry, and also high shlef will loose it's shape.
So cramped EQ has it's own 'sound' to it, especially in high frequency and it's different then 'quality' of EQ.
If this cramping is a issue for one, we can de-cramp it's frequency curve by adding shelf or adjusting Q and so on.
It will make frequency response of a EQ more matched to a analog EQ.
Compared to cramping EQ, decramped EQ will have more high frequency with same gain and Q, it 'sounds' more bright.
However, it causes the mismatch between phase and frequency response.
Since phase diffrence makes magnitude difference, I belive phase response matching frequency response affects how 'natural' a EQ sounds.
For example, a bell curve is made from a zero crossing phase response at it's peak frequency, not the other way.
In this manner, de-cramped EQ might feel more unnatural than cramping EQ.
So, cramping EQ will sound less airy and less analog than decramped one, but matches frequency and phase response.
decramped EQ will sound more like an analog EQ frequency-wise, but relation between frequency and phase response is lost.
Now, the oversampling solves both issues.
It decrampes both frequency and phase response, in cost of CPU and latency.
Moreover, with clean digital EQs without nonlinearity, oversampling half band filters does not have to be strong.
10 - 20 sample latency for x2 oversampling, 20 - 30 sample latency for x4 oversampling is enough for EQ.
Oversampled EQ will sound analog due to it's matched curve in high frequency, and naturalness of EQ is also preserved as frequency-phase relation is not touched!
3. How it behaves
The 'Feeling' of an EQ was more important than I thought!
Professional mix engineers, they don't turn on Plugin Doctor while mixing.
Also, they don't rely on EQ curve and frequency display either.
They look at values what plugins show and listens how it sounds while turning knobs, and thats all.
Then, shouldn't we focus on 'what values are showing' and 'what happens when we turn knobs?'
Let's look at Gain - Q dependency first.
It means turning gain knob affects Q value internally.
EQ with minimal Gain - Q dependency will remain relativly high Q in low gains, feeling clinical.
EQ with moderate Gain - Q dependency will have broad Q in low gains, feeling musical.
They will sound exactly same if we match gain and Q in Plugin Doctor! However, any engineer using these two EQs will say that they sound different, because the difference in Gain - Q dependency made them use EQ diffently!!
Another thing that we should look into is the Shelf Definition.
Many analog EQs and digital EQs with reputaion of nice highs have something in common.
They use specific definition of shelf filter: 6dB/oct first order filter for shelves, with frequency centered at -3dB point.
This is commonly missed point in digital EQs.
They make shelves in 12dB/oct and frequency centered at mid point, because this is how RBJ style shelves are defined.
So, what happens here? 6dB/oct filters are more shallow and much wider than 12dB/oct.
Also, at same displayed frequency, -3dB point shelf makes much lower shelf then -6dB or mid point shelf.
Since the magnitude changes gradually, starts early and ends late, it feels 'transparant' and 'smooth'.
These choices in filter design and UI will guide a specific way of using an EQ, making the perception of 'they sound different'