Apologies for the potentially simple question in advance. I have a limited understanding of the subject, but need to apply this to a project on short notice.
My goal is to run a DFT on a signal with N points and sample rate of R. The signal is often much shorter than 1 second, hence R is much larger than N. This causes the resulting DFT bins to skip many frequencies I'm interested in. As I understand, bin intervals are related to R/N, so I need to either increase N or decrease R. I was thinking about trying one of the following:
Stretch the signal by adding intermediate points which are averaged between real points so that N is large enough, then transposing the resulting frequencies back down by the stretch factor.
Appending to the signal with either 0s or another copy of itself to increase N.
Downsample the signal to lower R.
Are any of these ideas reasonable? I can not gather more points of the signal.
Edit: forgot to mention that the frequencies I'm interested in are very low (~20-300hz), so lowering the sample rate (usually 44.1k) shouldn't be an issue.