I'm trying to get a handle on the importance of the error feedback term in noise shaping operation in typical audio dither algorithms.
I'm thinking in terms of four signals. The original signal, the output (quantised) signal, the dither signal, and the error signal (the difference between output and original).
A simple approach would be to generate white noise and apply a filter to it to generate a coloured dither signal, add this to the original signal, quantise to the output signal, and disregard the error signal. It appears to be a fairly common approach to use white (unfiltered) or violet (differentiated) noise functions in this configuration.
Another approach I see implemented is to take the error signal and filter that and add white noise to define the dither signal, then add it to the original, quantise, and calculate the next error term for the filter. This implies a tight loop for the data flow -- we cannot compute a new error term without resolving the previous one -- making it hard to use SIMD efficiently.
From those I can infer a third option -- forgo the noise altogether and simply filter and reintegrate the error signal directly. I suppose this comes with some risk of modulation artefacts related to but distinct from the artefacts introduced by quantisation without any dither or shaping at all; however, I suspect this might be how it's done in some high-frequency 1-bit cases.
The point I'm unclear on is that complex filters which attempt to model the threshold of human hearing appear to come under the title of 'noise shaping', and this implies (supported by implementations I have seen) use of the error feedback term.
Is it a flawed or misguided approach to forgo the error feedback but still use the complex filter on white noise for the dither function? Is the error signal genuinely offering something important here?