# BW of a modulated signal

I come across different types of bandwidth. In digital modulation should it be null to null always? when do we use 3 db bandwidth?

• By "null" do you mean any frequency at which the power goes to zero, and then possibly bounces back up, or do you mean the point at which the power diminishes to zero and stays there? – TimWescott Aug 10 '20 at 15:04
• Null is where it first touches zero. – Mike Aug 10 '20 at 15:20

It's whatever makes the most sense for the problem at hand. Which can get confusing, and the same signal may have multiple definitions of "bandwidth" -- sometimes even in the same document, when, for example, one is reading up on or designing a communications system.

Useful Bandwidth

A signal's user is interested in the practically useful bandwidth of the signal, i.e., if it's analog can I fit comms-quality audio (300-3000Hz) on it, or hi-fidelity audio (20-20000Hz), or video (0-4.5MHz for old-style NTSC, and yes, that's debatable), and if it's digital what symbol rate could I achieve.

That 3dB point you're wondering about is often taken to be a signal's useful bandwidth.

Occupied (or assigned) Bandwidth

How much bandwidth the signal takes up in reality. This is the amount of bandwidth that you need to assign for the signal in the real world, so that signal A doesn't interfere with signal B when you're using real-world equipment. Typically occupied bandwidth is considered to be the bandwidth within which some large percentage (99%, 99.9%, etc.) of the total energy is confined, and in regulatory documents its usually defined in a way that makes it easy to test with reasonably-expensive instruments (i.e., a high-quality but not necessarily lab-grade spectrum analyzer).

Equivalent Noise Bandwidth

This is more a property of filters or systems, but the noise bandwidth of a filter is -- assuming the filter gain is normalized to 1 -- the ratio of the total noise power out of the filter to the total noise power in. So, for example, the equivalent noise bandwidth of a 1$$^{st}$$-order lowpass filter with a 3dB point at $$f_0$$ is $$\frac{\pi}{2}f_0$$.

Whatever

Sometimes, in the context of your work, you'll come across some other bandwidth that you wish to define (such as null to null). In that case, you state so clearly, and you use that as "bandwidth". So if you run across some screwy bandwidth definition, accept that the author has their reasons, understand it, and roll with it.