I'm trying to clear up some conceptual confusion I have about digital signal processing.
Say I have a 1000 point digital signal (stored in the memory of my arbitrary waveform generator "AWG"), and I set the AWG to read the signal out at 50 MHz. So every sample is getting played uniformly at 50MSa/s.
How does the rate that I set my AWG to play this signal at (50 MSa/s) determine the bandwith of my signal? I am familiar with the Nyquist sampling theorem as it applies to sampling an analog signal, but not how it applies to reconstructing a signal from digital samples.
Does the actual data (raw amplitude values) in the signal affect this signal bandwidth at all? I'm imagining the AWG playing a sequence of values [0 0 0 0 0 0 0 A 0 0 0 0 …], and if A is really large, wouldn't the DAC need a faster rise time to reach a higher amplitude value compared to if A was small (less energy it would need to dissipate)? This makes it seem to me like the amplitude values contained in the waveform would affect the rate the AWG is playing them out at, but this has nothing to do with the AWGs sample rate??
Thanks in advance for the help
Best Answer
Capturing digital samples is a form of recording. Playing them back at a rate faster than the recording rate has the effect of frequency shifting the entire spectrum toward higher frequencies.
If you record a 100 Hz audio tone and play it back at 2x the original sample rate, it will become a 200 Hz audio tone. Etc. Hopefully this is enough information for you to understand the concept.
There are techniques which would allow you to playback audio faster, but with the same perceived pitch.
And it is also possible to "re-sample" a data series at a higher frequency, so that it can be played back at a different sample rate, and sound basically identical. But the re-sampling process cannot add new information. It is just a form of interpolation.