Something about IIR Filter Co-efficient Normalization

If you're implementing an IIR filter then you are more constrained -- you
are designing a feedback loop, and the gain around the loop determines
the loop performance.  So if you normalize the coefficients to fit (and
you often do) you have to renormalize the result before you use it.  

Further, coefficient precision can have an impact on your filter
performance, as can the precision of the intermediate calculations.

Normalization matters in fixed-point arithmetics, where one wants to avoid underflow and overflow and so on.

You don't need to normalize filter coefficients to 1 under fixed point. 

There are three normalization method typically (cited from MATLAB help):

1. sum of the coefficients means that the sum of the coefficients equals 1

2. filter energy means that the sum of the squares of the coefficients equals 1;

3. peak amplitude means that the maximum coefficient equals 1.

What is the difference between the above three normalizations :

The first (with "magnitude" added) guarantees no internal overflow.

The second defines that the power of the output signal is the same as the power of a broadbanded input.

The third just says that you can represent your coefficients with fixed-point numbers (normally between -1 and +1) and have their relative values (to each other) be correct.

Normalization does not change the shape of the filter

Reference : http://www.hydrogenaudio.org/forums/index.php?showtopic=43195