For a project at work, I need to figure out the bandwidth requirements for a digital signal so I can spec components.
My first thought was to look at the Fourier Series for a pulse wave. I got so far as determining that the Fourier Series for a pulse wave or rectangular wave was something with the sin(x)/x function in it. I didn’t actually compute the Fourier Series myself I just found that information online – before I could attempt anything like that I found this rule that I had forgotten about. That the spectral content of a digital signal is related to the rise time. When I tried to use that "rule of thumb" for this project I found myself with a few questions.
Why is it seemingly universally recommended that you use the rise time to find the spectral content of a digital signal and not the Fourier Series representation? Seems that they would be equivalent, is it just that using the rise time is "easier"?
I can find the rise time for a signal easily with an oscilloscope, however, once I run that signal though anything, a longer cable, a coupler, an amplifier, a power splitter, an IC, won't the component affect the rise time of the signal? How do I know the bandwidth requirements of the signal after its gone through some component or device? How am I supposed to know the bandwidth requirement at any point along the signal’s path without directly measuring it after each component or device?
More Details: I have a 1.28 MHz clock signal, a pulse wave, that is already synthesized. It runs through a ~100' cable to a rack of electronics. I need to design a chassis that takes the signal, buffers it and distributes it, providing a copy of the signal for use at that area, and two more copies of it, to be sent through similar ~100' cables to be used elsewhere.
Best Answer
Because if you consider waveforms with different rise and fall times, they'll have different Fourier series (or Fourier transform) representations.
The width of the spectrum in the frequency domain will drop as the rise and fall times increase.
It depends on whether you've chosen those components with enough bandwidth to support the rise time you want to have for your signal.
Practically, it doesn't matter what the rise and fall time are at the signal source. More important is what rise and fall time you need to have for your receiver to work reliably. Then design your signal path with enough bandwidth to be sure that the rise and fall times don't get too slow before the signal gets to the receiver.