# Estimating the bandwidth of various signals

I am trying to estimate the bandwidth of different signals, with different modulations, as seen in a PSD graph. I've heard about a "$3\ \rm dB$ rule" in this context. I don't need extreme accuracy. Might drawing the edge of the channels at $3\ \rm dB$ down from the top work for me?

• well, that's pretty much what that 3dB rule says, isn't it? Anyway, I'm always a bit careful about that: for what purpose do you need to know the bandwidth? the 3dB rule makes sense when comparing modulations with similar spectra, but it doesn't make as much sense when comparing totally different spectral shapes! Thus the question: what do you use that bandwidth info for? – Marcus Müller Mar 3 '18 at 10:32

Another way would be fitting each of your signals' PSD with a Gaussian probability density function whose standard deviation $\sigma$ and mean $\mu$ you estimate, and use the full width at half maximum (FWHM) of this approximation as your half-power bandwidth. This is known accurately with the following closed form: $$\mathrm{FWHM}=2\sqrt{2\ln(2)} \sigma\approx 2.355\sigma$$ This approach is often used in practice to measure things like bandwidth expansion.