How to optimally normalize filter coefficients?
The OP should first implement the filter using floating point to confirm all specifications and structure. Once confirmed there is no &quot;optimal&quot; since the solution is a trade between precision required and accuracy needed in the result but typically the design approach is to use 2 more bits of precision for the coefficients over what is used in the datapath; scale all coefficients accordingly, let the filter grow the signal with an extended precision accumulator (such that no clipping occurs with input set to the maximum possible signal) and then scale the output back to the datapath precision.
See my further details on this at this answer recently posted:
What is the correct gain of an RRC Filter?