# Confusion about the meaning of Bandwidth-limited pulse

I am quoting Wikipedia: “A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth.”

But every pulse has minimum possible duration, so does that mean all pulses are bandwidth limited? Im superconfused here. Can you give me an example which illustrates the difference between bandwidth limited and not bandwidth limited pulse?

The more correct term is transform limited. That refers to a pulse that has the shortest possible duration for it's bandwidth.

Not all pulses are transform limited. Think of a burst of static for example. It has many random fluctuations up and down. Compare to a short gaussian pulse that rises up smoothly and then back down. If both have the same bandwidth, the latter pulse will be much, much shorter. This process can be understood formally using Fourier analysis, but that is the basic idea.

• I think I might have got it. Does that mean two pulses with different pulse durations can have the same freq. spectrum? And by having only the spectrum we can only obtain the possible shortest pulse duration? Jan 8 at 0:03
• @user1999 Yes exactly. For a given bandwidth, the shortest possible pulse is about 1/bandwidth. Jan 8 at 0:40

Yes, every pulse in the real world is bandwidth limited.

For example, an ideal square wave does not exist, as the vertical edge steps would require infinite bandwidth and thus infinite power to achieve.

Roughly, the narrower a pulse is in one domain, the wider it is in the other FT domain. In theory, any function with limited (finite) support in one domain is infinitely wide in the other domain. In practice, for Gaussian pulses and others, we ignore that tails that drop below some noise floor or numerical budget, and call some other property the width.

And a smooth Gaussian shaped pulse in one domain (of some "width") will have the most compact width in the other domain (for certain definitions of "width" and "compact").