I'm in an odd situation where an FFT is giving me too much data to process. I'm performing an FFT on audio sampled at 500 Hz, over 30 seconds. The result is 7500 bins of useful information, however I don't need this sort of resolution. I still need to see frequencies up to 250 Hz so I can't reduce the sampling rate. I also need information from the entire sample, so I can't use less than 30 seconds of data either.
What can I do to reduce the number of points, but keep the magnitude and phase information relatively intact? I would prefer not to throw away points, is it possible to take an average of x points?