Bitcrusher input gain

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Is there any difference to be made by gain staging a bitcrusher or boosting going into one that doesn't have input gain controls? Been playing around with bitcrushers recently and I've noticed that some offer an input gain control and some don't. I know that various types of distortion will provide different audible effects depending on the level of gain coming in. Is that true of a bitcrusher? Curious about the mathematics or anyone's experience/advice. My primary use case would be with drums, and I'm speaking to both the downsampling and quantizing (bit depth) functions.

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Turning the input up isn't going to do much on any bitcrushing plugin unless it has some kind of output stage. Since it's quantisation, you get the bitcrushing by turning the input down as the quantisation cannot accurately represent the amplitude at that scale and the samples become even moreso discrete at whatever bitdepth* you set

Samplerate reduction is linear as far as i understand. Aliasing wont change based on input volume in a dedicated decimation plugin, unless the aliasing is being produced by a nonlinear plugin with no oversampling. Try any old distortion plugin from the the early 2000's and drive it really hot. Can you hear them screaming kittens? BloodOverdrive is one particularly awful or awesome example of this depending on how you look at it
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Thanks for the helpful insights. I was mentally comparing with an overdrive, but knew that couldn't be correct. Hadn't even thought about reducing input gain, but something I will experiment with.

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