How to find the minimum no of bits required to express the filter coefficients in fixed point format from Histogram plot?

[himadri_debnath]

I have designed a filter in MATLAB and now I have to convert the filter coefficient in fixed point format from floating point format. For that my professor asked me to find histogram first and then find how many bits I required for fixed point representation. But I am not sure how to find that from histogram plot.

 

[danadakk]

First you have to have a criteria to work against, magnitude or phase or group
delay or.....that you will compare results against.

Say its magnitude, then we want a filter whose arithmetic does not saturate at
any node in the signal path, otherwise we have major distortion. IIR filters quite
involved on this topic.

Simple un-elegant way, look at max value filter is producing and pick
a binary size that can encompass that. Here your criteria is G of filter
at key freq of interest.

Or just pick 16 bits, run and compare the histogram against the floating point
result. Alter it up or down and see what works closest w/o being excessively large.

Analytically, there are reams of papers on net discussing numerical accuracy and effect
on pole zero locations for a filter, and to various criteria being looked. IEEE papers.....
and handbooks on digital filters.

There are other sophisticated ways of determining coefficients, like simple least squares,
or power curves or other estimation criteria, as stated at top of this post.

Your filter recursive or FIR ? Recursive can be very touchy to deal with.

Bottom conclusion comments -

https://www.eetimes.com/practical-applications-of-digital-filters/#

This page shows references to the topic at bottom of page -

Digital filter - Wikipedia

en.wikipedia.org

Regards, Dana.