# 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!

• Is there a specific paper or book you're using? Where is this formula from? Oct 24 '13 at 1:50
• Perhaps my knowledge is limited, but I never knew that bandwidth and bits used for representing a signal are related. Further, if noise is a deciding factor, I don't think we need to increase the number of bits, since noise in general may be white or have more high frequency content, which means that filtering only reduces the noise. Oct 24 '13 at 4:09
• It's from my mentor, he said it has something to do with the signal to noise ratio improvement since you filter out noise, hence you need to add a certain number of bits to achieve that Signal to Noise Ration. I really can't understand it quite well. Oct 25 '13 at 8:04