MP3 Psychoacoustic Cut-off Frequencies for Low-Bitrate Presets

Question

I've only seen frequency cut-off estimates for higher quality recordings. I'm interested in low bitrate frequency cutoffs:

• 24 kbps
• 32 kbps
• 40 kbps
• 48 kbps
• 56 kbps
• 64 kbps
• 80 kbps
• 96 kbps

I have a 96kbps 22.05kHz MP3 male speech recording that is clearly clipped at ~7.5kHz. My goal is to identify the probably original bitrate.

At 22.05kHz, anything above the nyquist frequency of 11.025kHz will be severely attenuated. The cut-off line at ~7.5kHz can't be caused by this unless the file was originally sampled at 15kHz, which is incredibly unlikely. Furthermore the resampling should leave some attenuation above 7.5kHz, so this looks more like a cut-off filter.

Nor is the ~7.5kHz cut-off inherent to human speech. According to second-hand excerpts of the MP3 reference material, a german male audio-clip frequenty spikes to 20kHz. Here is a 192kHz recording of a japanese female speech which regularly spikes to 50kHz

I'm aware that the cutoff frequency of the mp3 psycho-acoustic filter is unrelated to the mp3 bitrate. But pretty much every (and I mean every) mp3 file uses presets. And it seems that the presets of different encoders have similar cutoff frequencies.

Answer 1

Here is a tentative answer based on the 192kHz 24-bit Japanese female speech sample:

First I generate the test files from the sample file, sample02.wav:

for br in 8 16 24 32 40 48 56 64 80; do
    for lq in 0 2 5 7 9; do
        printf -v f0 "out_b%02d_q%d" "$br" "$lq"
        lame -b "$br" -q "$lq" sample02.wav "${f0}.mp3"
        sox "${f0}.mp3" -r 96k "${f0}_96kHz.wav"
    done
done

I limit the resampling to 96kHz to minimize the spectrograph's vertical bin size. For each q0 quality, here are my objective observations. To save time I didn't analyze the other qualities, though it is interesting to note that -q9 disables the psy-model. I try to ignore frequency spikes resulting from MP3's CBR bit reservoir, but this is just as subjective:

• bitrate: 08 quality: 0:

  • cutoff: 3187-3281
  • attenuation (from resampling, above the cutoff): 4125-4218
  • notes: aliasing obvious

• bitrate: 16 quality: 0:

  • cutoff: 5718-5812
  • attenuation (from resampling, above the cutoff): 6093-6187
  • notes: aliasing improves

• bitrate: 24 quality: 0:

  • cutoff: 6000-6093
  • attenuation (from resampling, above the cutoff): 6375-6468
  • notes: aliasing improves

• bitrate: 32 quality: 0:

  • cutoff: 8343-8531
  • attenuation (from resampling, above the cutoff): 8812-8906
  • notes: aliasing about the same

• bitrate: 40 quality: 0:

  • cutoff: 10687-10781
  • attenuation (from resampling, above the cutoff): 10968-11156
  • notes: aliasing improves

• bitrate: 48 quality: 0:

  • cutoff: 11250-11343
  • attenuation (from resampling, above the cutoff): 11812-11906
  • notes: aliasing about the same

• bitrate: 56 quality: 0:

  • cutoff: 15187-15281
  • attenuation (from resampling, above the cutoff): 15375-15468
  • notes: aliasing improves

• bitrate: 64 quality: 0:

  • cutoff: 16031-16218
  • attenuation (from resampling, above the cutoff): 16875-16968
  • notes: aliasing about the same

• bitrate: 80 quality: 0:

  • cutoff: 16125-16312
  • attenuation (from resampling, above the cutoff): ???
  • notes: aliasing improves

Judging by this I'd say my file was originally 32kbps. It will be interesting to see results from other encoders.