# Is it necessary to scale a signal for quantization noise analysis?

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.

Many Thanks

It makes sense to simulate the filter with a range of inputs that covers the space that you're designing the system to operate with. If the inputs will always be in the range $[-1, 1]$, then simulate using that range. On the other hand, if it's very likely that the data will be in that range, but possible that it might be larger, then it would be appropriate to test at higher levels. This requirement would likely be driven by higher-level considerations in your design.