I am doing a series of tests to analyse the round-off (quantization) noise performance of single and two stage biquad cascades (direct form 1), at different sampling rates. The system I am simulating for this analysis uses 8.24 fixed point arithmetic.
At the moment the expected data for the filter will only range between 1 and -1, and no scaling will be implemented for the time being, to make use of the upper bits. The analysis I am doing uses a white noise signal.
Is it necessary to scale the stimulus up to the full bit depth of the filter, in order to get an accurate measure of the round-off noise of the system?
As I do not expect the filter to overflow in practice due to the massive headroom available, I am not sure if there is a more appropriate amplitude to scale the signal to, that exercises the most bits without causing an overflow.