I know the question has been asked about why it's a bad idea to zero bins in an FFT, but those all seemed to be taking the IFFT afterwards. What if I want to do all my analysis in the frequency domain? Then would it be alright to zero the bins with frequencies i don't care about, and then perform my analysis?
And to add to that, if I only care about a certain range of frequencies, can I perform the DFT instead of an FFT, but were I'm only calculating the bins that I care about (I believe this should be the same as zeroing out all the other frequencies).
For example, lets say I have a signal sampled at 16000Hz. and the frequency range I care about is between 2000-4000Hz. if I'm taking a 64 point FFT/DFT, then I only care about bins 8-16. Since my signal is real, that should save some time on the DFT (real number multiplied by complex number as opposed to two complex numbers multiplied), and then I just do 9 DFT calculations and forget about the other 55. I think this should be less memory need and should perform the calculation quicker. I think this is right, but I'm probably missing something. Thanks for your time!