# Smart way to sample in "time domain" for a known "frequeny domain"

I have an experiment in which every point in the "time domain" is very expensive to take. Good news is I know the center frequency and the bandwidth of the signal.

How can I sample (which times should I probe) in the time domain to get the most information about the frequency range of interest with the least amount of points?

Is there some known method I can look into? If anyone has any resources/tutorial on this, I would be very grateful if you could point me towards them.

EDIT 1:

Please provide more details on your experiment, the actual expected frequency bandwidth and why the time domain samples are "expensive". Depending on the context the best answer will be very different. – Dan Boschen

In the actual experiment the "time domain" is a voltage that we use to manipulate electron spins. The Fourier transform of the spin response to the voltage gives us information about the spins surroundings (its just a blob in this case, but could have sharper features). I am attaching some real data (that encompasses the entire "frequency" range) so you get a sense of the center "frequency" and bandwidth.

The sampling is "expensive" because each pulse voltage needs averaging, taking a few minutes, and we would like to make this as fast as possible. Intuitively, its clear that we are oversampling as there as many points with a value of 0, hence the question.

• hey, this is a typical homework question. And the answer is: You'll learn about mixing and probably about equivalent baseband in just 4 or 5 pages of your textbook! Oct 27, 2019 at 11:09
• Could you please let me know what textbook is good for this? I am really trying to do an experiment, not homework or anything like that. And never really had any formal education in these sorts of problems. Oct 27, 2019 at 11:15
• Please provide more details on your experiment, the actual expected frequency bandwidth and why the time domain samples are "expensive". Depending on the context the best answer will be very different. Oct 27, 2019 at 11:28
• @Gyromagnetic hm, all textbook for German Nachrichtentechnik 1 (or equivalent) lectures would fit that description. If you don't have access to one of these: "equivalent baseband" is very well-explained in a lot of places. What's your background? Physicist? Oct 27, 2019 at 11:46
• It seems that would achieve your objective--- you can test this by truncating the result you have and seeing the result-- you will have less of the not useful flat area in your frequency. Therefore you can do more runs in the voltage range of interest (0 to 1). Does that make sense? Oct 27, 2019 at 12:48