I'm implementing a scattered look-ahead IIR filter in Matlab/VHDL, basically I convert an order-2 IIR filter into an order-4 IIR in order to take advantage of the pipelining of an FPGA. (reference http://people.ece.umn.edu/users/parhi/SLIDES/chap10.pdf)
Anyway, I'm trying to evaluate how many bits I need in every stage and I was wondering if there is a metric to evaluate the "quality" of the quantization.
For example an error of 0.1% in the transient of a step response doesn't matter much but a a neverending limit cycle of 0.1% after the transient would be a problem.
I was thinking of using a metric like m = error^2 * n
where error is the difference between the reference double implementation and my fixed-point implementation and "n" is the sample number so an error at sample 100 would weigh more than error at sample 1.
I would need to balance quantization errors with FPGA resources and FPGA speed of course.
Are there other metrics? Am I on the right track?