Deriving the 1 bit = 6 dB rule of thumb

December 9, 2008

This week, a more mathematical topic. Sometime ago, we—friends and I—were discussing the fidelity of various signals, and how many bits were needed for an optimal digitization of the signal, given known characteristics such as spectrum and signal-to-noise ratio.

Indeed, at some point, when adding bits, you only add more power to represent noise in the signal. There’s a rule of thumb that say that for every bit you add, you can represent a signal with $\approx 6 dB$ more of signal to noise ratio. Let me show you how you derive such a result.