Analysing 2500 frequencies using FFT with an input vector of 2048 samples? I am currently reading the paper A Highly Robust Audio Fingerprinting System and on page 4 one can read about the technical parameters they use: Sampling rate of 5000 Hz, frames of 2048 samples as input to the FFT and with these settings they analyse frequencies from 300 Hz to 2000 Hz. Here are the respective quotes:


  Since  the  algorithm  only  takes  into  account  frequencies 
  below 2kHz the received audio is first down sampled to a mono 
  audio stream with a sampling rate of 5kHz.


.


  The most computationally demanding operation is 
  the Fourier transform of every audio frame. In the down sampled 
  audio signal a frame has a length of 2048 samples. 


.


  These bands lie 
  in  the  range  from  300Hz  to  2000Hz 


What I don't understand: How can one analyse frequencies up to 2000 Hz using 2048 samples as input to the FFT? As far as I know the FFT output is mirrored, therefore with 2048 samples as input I get an output vector of length 2048, however what I can effectively really use are the first 1024 values (2048/2 due to mirroring). So I would have only 1024 values for 2500 different frequencies? (sample rate is 5000 Hz and according to Nyquist maximum possible frequency therefore 2500 Hz)

Thanks for any hint!
The first 1024 output bins of the FFT represent frequencies from 0 Hz to Fs / 2 = 2.5 kHz. So each bin is 2500 / 1024 = 2.44 Hz wide. In other words you have a resolution of 2.44 Hz in the frequency domain.