Effect of bandwidth reduction in bit growth I just want to ask, whenever you reduce a bandwidth of signal by filtering, I wonder why do you need to improve the number of bits used to represent that signal.
The number of bit growth is 
$$\frac{1}{2}\log_2\left(\frac{BW_{in}}{BW_{out}}\right)$$

Is it to represent to small noise due to filtering.
Thanks!
Consider a two-sample moving average of one-bit data with values {0,1}. The bandwidth is reduced by a factor of two. The possible outputs are {0,0.5,1}. You have gained half a bit, as predicted by the formula.

John